## Solving Quadratic Equations – Use Algebra Calculator

Algebra is one of the important parts of mathematics, and it is right to say it is an essential branch of mathematics. Algebra includes three common parts in their equation such as unknown parts which are known as variable, coefficient and number values. According to the degree available in the unknown part, the algebra is known as a different name such as a linear equation, polynomial equation, quadratic equation, cubic equation, exponential equation and much more. Thus, the algebra is a large part of mathematics. Here we are going to learn solving quadratic equations in different methods.

It is one of the algebraic equation which includes two factors or roots of unknown value. If learn simply, the standard format of quadratic equation is-

ax² + bx + c = 0

Here the standard format of a quadratic equation is visible where you can find variable (x), constant or number term (c) and coefficient of x²  and x i.e. a and b.

Now solving the quadratic equation is quite simple with the latest algebra calculators but slightly difficult if solved by formula methods. Different methods you can use to solve the quadratic equations in which formula method is explained below in the content.

Consider an example to learn how to solve quadratic equation by formula method

x² + 3x – 4 = 0

Formula to identify the unknown term is: -b ± √b²-4ac⁄2a

According to the standard format of quadratic equation a = 1, b = 3 and c = -4

Put these values on the formula to find the value of a variable. You will get,

x = -3 ± √9 – 4.1. (-4)⁄2.1

x = -3 ± √9+16⁄2

x = -3 ± √25⁄2

x = -3 ± 5⁄2

Now, you can consider mathematical signs separately to identify both values separately that can balance the whole equation. Follow steps given below-

x = -3 + 5⁄2

x = 2⁄2

x = 1

And,

x = – 3 – 5⁄2

x = – 8⁄2

x = – 4

Now, you have two separate values of variable, i.e. x=1 and-4

This is formula method to solve any quadratic equation. It is quite simple, but you have to perform a much mathematical operation like multiplication, division, subtraction, and addition too. Also, you use other methods for solving a quadratic equation. In the quadratic equation, there are two roots are available that can balance the whole equation. Consider the same example to learn the root method of solving quadratic equations.  x² + 3x – 4 = 0

Here a = 1, b = 3 and c = – 4

To find out the variable values, use particular formula as-

α + β = – b⁄a

α β = c⁄a

Put the values to get the values of α and β

α + β = – 3⁄1

α + β = – 3

And

α β = -4⁄1

α β = – 4

Square both the term of ∝+β to find out unknown values as

α² + β² + 2αβ = 9

Now,

(α – β) ² + 2αβ + 22 αβ = 9

(α – β) ² + 2αβ + 22αβ = 9

(α – β) ² + 4αβ = 9

Put the values of α β in the above equation

(α – β) ² + 4 * – 4 = 9

(α – β) ² – 16 = 9

(α – β) ² = 25

α – β = 5

Now add α – β and α + β

You will get

2α = 2

Then

α = 1

Put the value of ∝ in any above equation

You will get

β = -4

Hence, you have a choice to use different methods to solve a quadratic equation. On the other hand, you can choose the algebra calculator that can easily find out variable values and deliver results in fast. In the algebra calculator, you just need to enter the quadratic equitation on the required field in the calculator. Thus, enter one next tap to solve the equation. The calculator solves the equation with the genuine method, and there is no short answer you will get. Thus, solving quadratic equations is quite easy with the calculator.

## Solve for X – Easy Methods to get the Value of X

If you are looking for different ways via which you could solve for x, then you are welcome here. The content is meant for those students who face problems while solving radicals and exponents in algebra. After reading this content, you will get the right method to solve it. So, let’s start this learning session.

Basic linear equation

We are going to solve simple linear equation 5x – 8 = x + 4 and find out the value of X.

Step 1: At first, we will arrange 5x and x on the left-hand side and 4 and on the right-hand side.

5x – 8 = x + 4

Step 2: After that, we will solve the arrange number and here is the further procedure:

Important note: Before solving any equation, students should solve exponents if there is any to make the equation easy.

Solve it by isolating the terms (in case of exponents)

If you didn’t get it as what I meant by the word “isolating” then here is an explanation for you. It means that you should make one term disappear to get the value of X. The trick is quite popular plus makes the procedure easy. So, how to solve for x by this method?

Example: 2x² + 14 = 46

Step 1: In the above example, we are going to isolate term 14 and thus we ill subtract both the sides by 14.  Keep in mind that you should choose an opposite side for isolating a term, i.e., here 14 is positive and thus we have chosen (-14) in it.

2x² + 14 – 14 = 46 – 14

2x² = 32

Step 2: Now you see that number 14 has gone and now we can find the value of x easily. Here are its further steps:

Now, we know that 16 is the square of 4 and thus we will square root both the sides and get:

x = 4

Solving fractions by cross multiplication method

Fractions are easy to solve, by using multiplication methods we can get the value of X. So, here is the example:

Step 1:  We will solve this by cross multiplication method where we will multiply 4) by 4 and 3 by 4.

(x – 4) (4) = (2) (4)

4x – 16 = 8

Step 2: Now we will combine the like terms like this:

4x = 8 + 16

4x = 24

X = 24 ⁄ 4

And finally, we get x = 6. The cross multiplication method is very easy but does not forget to reduce the problem into simplest form.

Solve for x using radical signs

For this one, you need to learn some basic concepts of radical sign or square roots. Now, let’s solve example

Step 1: In the first step, we will isolate the number 5 by adding 5 on both the sides like this:

Step 2: Now we are going to square both the sides:

Step 3: Again, we will subtract both the sides by 7 so that 2x remain on the LHS:

So, we have got the answer 9, and you can verify this answer by putting the value of x in the problem.

Hope so all the methods explained above let you solve for x easily and make your mathematics stronger.

A lot of people are terrified when they are required to add fractions. Many even take out a calculator, convert the fractions to decimals and add them together that way. Don’t worry, though; adding fractions is not nearly as difficult as many make it appear. The best thing about knowing how to add fractions is that once you know how to add fractions, you can subtract them from each other just as easily.

This is very important: The key to adding fractions is to make sure that the denominators of the two fractions you are adding (the numbers on the bottom) are equal. This is not necessary for fraction multiplication, and thus it is a source of confusion for many.

Before you attempt to make the denominators the same, it is advisable to put both fractions in lowest terms (also called simplifying). Now, in order to make the denominators equal, you’re going to want to multiply each denominator by the opposite denominator. Keep track of what number you’re multiplying each denominator by, as you’ll need to multiply the numerator of the fractions by that number as well. Once you’ve done that, you simply add the numerators. In practice, this looks like 3/4+1/7=(7/7)*(3/4)+(4/4)*(1/7)=21/28+4/28=25/28

There are other ways to equalize the denominators, but this is a technique that works in all cases in which you are adding two fractions together. To add more than two fractions, it is easiest to add two together and then add that result to the third (that will keep the denominator “juggling” simple).

A lot of people are terrified when they are required to add fractions. Many even take out a calculator, convert the fractions to decimals and add them together that way. Don’t worry, though; adding fractions is not nearly as difficult as many make it appear. The best thing about knowing how to add fractions is that once you know how to add fractions, you can subtract them from each other just as easily.

This is very important: The key to adding fractions is to make sure that the denominators of the two fractions you are adding (the numbers on the bottom) are equal. This is not necessary for fraction multiplication, and thus it is a source of confusion for many.

Before you attempt to make the denominators the same, it is advisable to put both fractions in lowest terms (also called simplifying). Now, in order to make the denominators equal, you’re going to want to multiply each denominator by the opposite denominator. Keep track of what number you’re multiplying each denominator by, as you’ll need to multiply the numerator of the fractions by that number as well. Once you’ve done that, you simply add the numerators. In practice, this looks like 3/4+1/7=(7/7)*(3/4)+(4/4)*(1/7)=21/28+4/28=25/28

There are other ways to equalize the denominators, but this is a technique that works in all cases in which you are adding two fractions together. To add more than two fractions, it is easiest to add two together and then add that result to the third (that will keep the denominator “juggling” simple).

As mentioned earlier, subtracting fractions is just as easy. All you have to do is equalize the denominators and subtract the second numerator from the first numerator.

## Fraction Calculator

Fractions can be way difficult to absorb for some students when they first start with the topic. Especially, when dealing with equivalent fractions; it seems that they do not get the head or tail of anything. The concept in reality is very simple; but if the logic still eludes you, you can try using an equivalent fractions calculator, till you get the hang of it.

Your math teacher tells you the equivalent fractions are two or more fractions that have the same value, but have different forms. In simple words, these fractions can be defined as fractions having the same overall value, or the same simplest ratio. These fractions indicate the same part of a whole. The easiest way to explain equivalent fractions is using the example of a round apple pie. Whether you divide a pie into two pieces and take one, or out of four pieces take 2, or further on out of 8 pieces take 4; you still get one-half of the pie to eat. So we can conclude that 1/2 is same as 2/4 or 4/8; they all are equivalent fractions.

The technique to simplify a fraction is very easy; both numerator and denominator must be divided by the same number to reduce the fraction. So remember that the value of a fraction does not change if you multiply or divide the whole fraction by the same number. Remember that the number you use for division must divide without leaving a remainder. Both the numerator and denominator of a fraction must always be whole numbers; so you can know when you have arrived at the simplest answer & cannot reduce the fraction any further. And remember, only multiplication and subtraction is valid when reducing fractions; do not try to perform addition or subtraction while reducing your fractions.

The easiest way when working with conference is to use fraction calculator to check your answers. This will boost your confidence & in the long run help you with your math homework. But remember, that using these calculator will only validate your answer; you still have to learn how to arrive at that answer in the first place.

The prized scientific calculator of your elder sister can act as your equivalent fractions calculator; you can easily check your answers using it. On the other hand, there are many math websites today offering their own version of equivalent fractions calculator, you can easily search & bookmark your favorite one to verify your answers. You can also ask your nerd brother to write a short program for an equivalent fractions calculator; whether he uses C++ or Assembly, the code to develop these calculators is very simple.

It is always important that you make sure that you visit a reliable site to do your calculations. There are some sites that tend to rob your money. It is always important that you do your homework well before choosing a site, to be in a safe situation it is ideal that you go for those sites that have reviews.

## How to Solve For X in Equation

Sometime the equation may contain the letters and not the number. It may be daunting and may students worry when they hear the word algebra.  Sometime algebra can turn to be hard since you have to deal with unknown amounts and the math will not be that concrete anymore. However, the best place to start with is starting with the basic foundation, and you can then learn how to solve for x.  This means that you may figure out how much the unknown amount should be.

The basic rule is that the first step which you have to take to solve for the x is to get the x on its own and alone. At one side of an equation, everything else will be at the one side. You have to keep in mind the rule, what you need to do at one side of an equation, has to be done at another side.  This is to ensure that the equation continues to be equal.

You should start with the simple equation. The basic algebra equation will involve some simple subtraction and addition that have unknown quantity.

As you continue to learn algebra, you will have to go from the simple equation and use an equation that has even more steps. The more difficult equation will have different equations.

As you continue to get more information about how to solve the equation, it will be easier for you to solve for these letters. If you would like to be comfortable by working on algebra problems, then you should take time to practice.

Whenever students are asked to solve for x, they may assume that there is always the solution for x.  However, this is not always the case. When the solution is resolved, sometime the final results may not be achieved.

If you worry about algebra, then you have to know that it is the extension of the basic arithmetic which you are using on a daily basis.  If you know the basic, then it will be easy.  As you practice more, then the rules are going to be automatic.  If you do encounter the problems, you will then find out that rules and tricks to use in order to solve for x.

You should review the basic mathematics and arithmetic. Even when you remember the negative numbers, you can add the fraction, do the practice sets and this will boost your confidence.  When it comes to algebra, you will need to perform the basic operation, but now there are letters mixed with the equations. The letters are called the variables.   When you have to solve algebra, you will have to find the value of a variable.

When you solve for x, you will have to combine. First the like terms and these are terms that have same variables.  When your multiply or divide a term, you should do it on both sides of the equation. When you reach to the last solution, it will be called factors of a solution.  Factoring in the algebra is breaking down things that seem to become even more complex.  When you break down items in smaller pieces, you will have to apply the math skills and to find answers.

## What are a Quadratic Formula Calculator and its Standard Equation?

In elementary algebra, there are various ways of solving a quadratic equation such as completing the square, graphing or factoring. However and whenever you seek for a way to solve these equations the best way which comes to your mind is the Quadratic formula calculator. That is a one-step solution for all kind of quadratic equations. It is one of the simpler, easiest and convenient ways of solving equations. After reading this article, you will become able to identify a quadratic equation. You will learn how to place a quadratic equation into a standard form along with learning the alternative ways to derive a quadratic equation general formula.

A quadratic formula calculator in general terms could be called as a polynomial equation which contains the second degree and no higher degrees of a variable. The standard form of a quadratic equation is –

mx² + nx + k = 0

In this equation, the value of x is always unknown. m, n, and k are constant in which they should be equal to 0 or contains some negative and positive values. On the way to verify whether the quadratic formula is satisfying a quadratic equation or not, you have to insert the former one into the latter. This is known as parameterization. After this, the general quadratic formula is converted into

All the quadratic equations can be inserted in a standard form. And any equation which can be put into a standard form and can be solved by a quadratic formula solver represents a quadratic equation. The solution of any equation is sometimes known as the root of an equation.

There are various methods for deriving the quadratic formula. Some of these may either be simpler than completing the square method however the method represents interesting applications of the different algebraic techniques. It offers a different view of the field of mathematics.

How the general quadratic formula calculator is derived?

mx² + nx + k = 0

4m²x² + 4mnx + 4mk = 0

4m²x² + 4mnx = -4mk

4m²x² + 4mnx + n² = n² – 4mk

(2mx + n)² = n² – 4mk

This is an ancient way of determining the quadratic formula which was known to the people around years ago. When it is compared with other ways of deriving the standard formula, this way of solving and determining the formula is quite simpler. The benefits of this formula derivation are-

• Simple to solve and is less complicated
• Less computation of literal coefficients
• It does not involve fractions until the very last steps.
• Use of simple math with simple expressions
• The central theme of algebra is to solve the equations

However solving these equations is not easy for everyone. A lot of times people find a problem get stuck into a particular quadratic equation and do not find the way to solve it. The basic command over mathematics is a must to solve such equations. However, there are various sites which are now offering the services of instantly solving the equations. One such site is the Quick Math which allows you to put down your equation in the available dialogue box to provide the quadratic formula calculator. The whole solution can be displayed along with the answer. It makes your math problems easier and explains the alternative ways to solve an equation.

## Learn to Solve a Linear Equation Perfectly

Mathematics is known to be a subject with lots of interesting facts with it. There are many who love to understand the subject deeply and know some more excellent facts about it. Algebra is the most important part of mathematics with some of the most interesting methods and formula. To be perfect in the subject one needs to be perfect with algebra.

Equations constitute some of the basic components, there are many who search out some of the best ways to get perfect in solving equations. If you are able you solve the equations well, then you can handle algebra very easily. Therefore here we are going to deal with the simplest, linear equation and the best ways to solve it correctly.  By the time you will get to know some more interesting tricks while solving such problems.

Thorough Basics

Before we move further, everyone should remember the importance of basics. If you are clear with the basics then only you will be able to handle the complex problems perfectly. Therefore it is the best that before moving on to the complex problems learn the basic tricks and formulae well. You need to use the right formula at the right place. You will soon be able to interpret this when you practice the problems regularly. Therefore have a look at your lessons and practice daily. This way you will surely be able to deal with algebra perfectly.

## Solving a linear equation

Isolating the variable is the major part in the process of solving the linear equations when you get answers in the form y = 6 or x = 7. Here, the variable is brought to itself or is separated from the rest of the equation. But the question is, How to do this? Well, this may depend on several different factors. We will have to perform exactly the opposite of the operations that are done in the equation. This way you will be able to get the initial equation. Like if something is added we will subtract the same, or if something is multiplied, we will divide the same. All this has to be done considering the LHS and RHS rules. Here is the example of a one-step equation:

Suppose, 4x=8 ; Now to isolate the variable x, we will have to bring it to the other side which will result in the change of operation. Further, it will be:

x=8÷4 ; Therefore, x=2 . Thus isolating the variable will make it easy for you to get the answer.

A two-step equation

Now let’s see a two-step equation say, Solve 2y−7=13. The noticeable fact here is that the variable y is first multiplied by 2 and then 7 is subtracted from it. Therefore to cancel these effects, the solution will move like:

2y-7+7 = 13+7 (Add 7 to both sides as per the LHS and RHS rule) Now,

2y = 20 ; Now solving the equation further,

2y⁄2 = 20⁄2 (Divide 2 on the two sides of the equation) Thus,

y = 10

This way you can easily solve and get perfect with any kind of linear equation.