Algebra Examples

$y^{2} + x = 2$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y^{2} - 2 = 2$

Step 2

Solve the equation for $y$ .

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Step 2.1

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1.1

Add $2$ to both sides of the equation.

$y^{2} = 2 + 2$

Step 2.1.2

Add $2$ and $2$ .

$y^{2} = 4$

Step 2.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{4}$

Step 2.3

Simplify $\pm \sqrt{4}$ .

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Step 2.3.1

Rewrite $4$ as $2^{2}$ .

$y = \pm \sqrt{2^{2}}$

Step 2.3.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 2$

Step 2.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.4.1

First, use the positive value of the $\pm$ to find the first solution.

$y = 2$

Step 2.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 2$

Step 2.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = 2, - 2$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y^{2} - 1 = 2$

Step 4

Solve the equation for $y$ .

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Step 4.1

Move all terms not containing $y$ to the right side of the equation.

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Step 4.1.1

Add $1$ to both sides of the equation.

$y^{2} = 2 + 1$

Step 4.1.2

Add $2$ and $1$ .

$y^{2} = 3$

Step 4.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{3}$

Step 4.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.3.1

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{3}$

Step 4.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{3}$

Step 4.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{3}, - \sqrt{3}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y^{2} + 0 = 2$

Step 6

Solve the equation for $y$ .

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Step 6.1

Add $y^{2}$ and $0$ .

$y^{2} = 2$

Step 6.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{2}$

Step 6.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 6.3.1

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{2}$

Step 6.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{2}$

Step 6.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{2}, - \sqrt{2}$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y^{2} + 1 = 2$

Step 8

Solve the equation for $y$ .

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Step 8.1

Move all terms not containing $y$ to the right side of the equation.

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Step 8.1.1

Subtract $1$ from both sides of the equation.

$y^{2} = 2 - 1$

Step 8.1.2

Subtract $1$ from $2$ .

$y^{2} = 1$

Step 8.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{1}$

Step 8.3

Any root of $1$ is $1$ .

$y = \pm 1$

Step 8.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 8.4.1

First, use the positive value of the $\pm$ to find the first solution.

$y = 1$

Step 8.4.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - 1$

Step 8.4.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = 1, - 1$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y^{2} + 2 = 2$

Step 10

Solve the equation for $y$ .

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Step 10.1

Move all terms not containing $y$ to the right side of the equation.

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Step 10.1.1

Subtract $2$ from both sides of the equation.

$y^{2} = 2 - 2$

Step 10.1.2

Subtract $2$ from $2$ .

$y^{2} = 0$

Step 10.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{0}$

Step 10.3

Simplify $\pm \sqrt{0}$ .

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Step 10.3.1

Rewrite $0$ as $0^{2}$ .

$y = \pm \sqrt{0^{2}}$

Step 10.3.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 0$

Step 10.3.3

Plus or minus $0$ is $0$ .

$y = 0$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 2 \\ - 1 & - 2 \\ 0 & \sqrt{3} \\ 1 & - \sqrt{3} \\ 2 & \sqrt{2} \end{array}$

Step 12