# Variable Isolation Calculator + Online Solver With Free Steps

A Variable Isolation Calculator is an online tool that helps to solve equations for any given variable. It uses the reverse order of operations to segregate the variable on one side of the equation and move every other term to the other side. In algebra, one equation is solved for the desired variable by isolating it within the equation. Sometimes it is difficult to separate the variable within the equation because it has multiple terms involving the variable but they are not similar. For example, in the equation given as:

x^3 + 3x = 9

The variable x cannot be isolated simply by moving the terms. Therefore, it requires some special techniques and lengthy calculations. Such equations are sometimes complex to solve by hand, hence the Variable Isolation Calculator is here to help you.

## What Is a Variable Isolation Calculator?

A Variable Isolation Calculator is a calculator that is used to isolate the variable and solve the equation for it.  It is an easy-to-use calculator that can be used to solve various algebraic equations for desired variables. The calculator works by isolating the variable of interest and applying various mathematical operations required. Algebraic equations are solved by changing or manipulating the subject (variable of interest). They are also called Isolating variables. For instance, the equation $4x^2 -9y = 2$ needs to be solved for calculating the value of variable x. So x is the isolating variable and the whole equation has to be modified in a manner such that variable $x$ is isolated on the one side of the algebraic equation.

## How To Use the Variable Isolation Calculator

The Variable Isolation Calculator can easily be used by following the simple steps mentioned below:

### Step 1:

First, enter the isolating variable for your desired equation in the tab named “Isolate for.”

### Step 2:

After specifying the isolating variable, input the equation in the “Equation” tab.

### Step 3:

Once you are done with the steps mentioned above, press the submit button.

### Step 4:

A new window will appear in front of you displaying the result for the equation. If you want to view the detailed solution to the problem, click the appropriate button on the screen and you can see the step-by-step solution as well.

### Step 5:

If you want to have the solution for any other equation, simply input the equation and press the submit button. You can solve as many equations as you want.

## How Does the Variable Isolation Calculator Work?

The Variable Isolation Calculator works by applying various mathematical operations to any given equation to solve for the specified variable. This calculator provides you the instant answers the moment you press the submit button. The calculator is created using JavaScript programming language powered by CAS. The calculator works by filtering the equation into CAS that solves it for the specified isolating variable by the user. Furthermore, it treats each word and number as a symbol and segregates the variable of interest in the equation. Once the final result has been finalized, it converts the result into the LaTeX format and displays it on the screen as an answer. There are various techniques used for isolating the variable within the equation. Some of them are discussed below:
1. Applying the same operation on both sides of the equation
2. Inverse operation

### Applying the Same Operation on Both Sides of the Equation

While isolating the variable within the equation, it is extremely important to make sure that both sides of the equation remain the same. For solving the equation, various mathematical operations are performed such as adding or subtracting any term or variable. But any operation performed on an equation must be done on both sides of the equation.  If a certain operation is applied only on one side of the equation, it will give rise to a false statement. Hence, to make sure that the given statement remains true, the mathematical operation must be performed on both sides of the equation.

### Inverse Operation

You can isolate a variable by canceling out operations on the same side of an equation while maintaining equality. This is done with inverse operations that remove terms needed to find the isolated subject (variable of interest), leaving it alone and making sure nothing changes in its value.  For instance, addition cancels subtraction and subtraction cancels addition. Similarly, multiplication cancels division and division cancels multiplication. These are called inverse operations of each other.

## Solved Examples

### Example 1

Solve the given equation for y. $y^2 – 8x = 2x$

### Solution

Figure-2 Example 1 solved

Put the expression in the calculator and isolate it for y. The results are shown as follows: $y = +\sqrt{10x}$ $y = -\sqrt{10x}$

### Example 2

Represent the following equation: $\sqrt{4x + 5y} = 100$ where x is the subject.

### Solution

Input the given in equation in the calculator and specify x as the isolating variable. The output is shown as: $2500 – \dfrac{5y}{4}$

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