Algebra Examples

$x = y^{2}$

Step 1

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

$- 2 = y^{2}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Rewrite the equation as $y^{2} = - 2$ .

$y^{2} = - 2$

Step 2.2

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

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

Step 2.3

Simplify $\pm \sqrt{- 2}$ .

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Step 2.3.1

Rewrite $- 2$ as $- 1 (2)$ .

$y = \pm \sqrt{- 1 (2)}$

Step 2.3.2

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$y = \pm \sqrt{- 1} \cdot \sqrt{2}$

Step 2.3.3

Rewrite $\sqrt{- 1}$ as $i$ .

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

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.

$y = i \sqrt{2}$

Step 2.4.2

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

$y = - i \sqrt{2}$

Step 2.4.3

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

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

Step 3

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

$- 1 = y^{2}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Rewrite the equation as $y^{2} = - 1$ .

$y^{2} = - 1$

Step 4.2

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

$y = \pm \sqrt{- 1}$

Step 4.3

Rewrite $\sqrt{- 1}$ as $i$ .

$y = \pm i$

Step 4.4

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

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Step 4.4.1

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

$y = i$

Step 4.4.2

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

$y = - i$

Step 4.4.3

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

$y = i, - i$

Step 5

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

$0 = y^{2}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Rewrite the equation as $y^{2} = 0$ .

$y^{2} = 0$

Step 6.2

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

$y = \pm \sqrt{0}$

Step 6.3

Simplify $\pm \sqrt{0}$ .

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Step 6.3.1

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

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

Step 6.3.2

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

$y = \pm 0$

Step 6.3.3

Plus or minus $0$ is $0$ .

$y = 0$

Step 7

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

$1 = y^{2}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Rewrite the equation as $y^{2} = 1$ .

$y^{2} = 1$

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 $y$ .

$2 = y^{2}$

Step 10

Solve the equation for $y$ .

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Step 10.1

Rewrite the equation as $y^{2} = 2$ .

$y^{2} = 2$

Step 10.2

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

$y = \pm \sqrt{2}$

Step 10.3

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

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Step 10.3.1

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

$y = \sqrt{2}$

Step 10.3.2

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

$y = - \sqrt{2}$

Step 10.3.3

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

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

Step 11

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

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

Step 12