Algebra Examples

$x^{2} + y^{2} = 25$

Step 1

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

${(- 2)}^{2} + y^{2} = 25$

Step 2

Solve the equation for $y$ .

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Step 2.1

Raise $- 2$ to the power of $2$ .

$4 + y^{2} = 25$

Step 2.2

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

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Step 2.2.1

Subtract $4$ from both sides of the equation.

$y^{2} = 25 - 4$

Step 2.2.2

Subtract $4$ from $25$ .

$y^{2} = 21$

Step 2.3

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

$y = \pm \sqrt{21}$

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.

$y = \sqrt{21}$

Step 2.4.2

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

$y = - \sqrt{21}$

Step 2.4.3

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

$y = \sqrt{21}, - \sqrt{21}$

Step 3

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

${(- 1)}^{2} + y^{2} = 25$

Step 4

Solve the equation for $y$ .

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Step 4.1

Raise $- 1$ to the power of $2$ .

$1 + y^{2} = 25$

Step 4.2

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

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Step 4.2.1

Subtract $1$ from both sides of the equation.

$y^{2} = 25 - 1$

Step 4.2.2

Subtract $1$ from $25$ .

$y^{2} = 24$

Step 4.3

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

$y = \pm \sqrt{24}$

Step 4.4

Simplify $\pm \sqrt{24}$ .

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Step 4.4.1

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 4.4.1.1

Factor $4$ out of $24$ .

$y = \pm \sqrt{4 (6)}$

Step 4.4.1.2

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

$y = \pm \sqrt{2^{2} \cdot 6}$

Step 4.4.2

Pull terms out from under the radical.

$y = \pm 2 \sqrt{6}$

Step 4.5

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

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Step 4.5.1

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

$y = 2 \sqrt{6}$

Step 4.5.2

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

$y = - 2 \sqrt{6}$

Step 4.5.3

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

$y = 2 \sqrt{6}, - 2 \sqrt{6}$

Step 5

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

${(0)}^{2} + y^{2} = 25$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify ${(0)}^{2} + y^{2}$ .

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Step 6.1.1

Raising $0$ to any positive power yields $0$ .

$0 + y^{2} = 25$

Step 6.1.2

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

$y^{2} = 25$

Step 6.2

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

$y = \pm \sqrt{25}$

Step 6.3

Simplify $\pm \sqrt{25}$ .

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Step 6.3.1

Rewrite $25$ as $5^{2}$ .

$y = \pm \sqrt{5^{2}}$

Step 6.3.2

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

$y = \pm 5$

Step 6.4

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

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Step 6.4.1

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

$y = 5$

Step 6.4.2

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

$y = - 5$

Step 6.4.3

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

$y = 5, - 5$

Step 7

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

${(1)}^{2} + y^{2} = 25$

Step 8

Solve the equation for $y$ .

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Step 8.1

One to any power is one.

$1 + y^{2} = 25$

Step 8.2

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

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Step 8.2.1

Subtract $1$ from both sides of the equation.

$y^{2} = 25 - 1$

Step 8.2.2

Subtract $1$ from $25$ .

$y^{2} = 24$

Step 8.3

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

$y = \pm \sqrt{24}$

Step 8.4

Simplify $\pm \sqrt{24}$ .

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Step 8.4.1

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 8.4.1.1

Factor $4$ out of $24$ .

$y = \pm \sqrt{4 (6)}$

Step 8.4.1.2

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

$y = \pm \sqrt{2^{2} \cdot 6}$

Step 8.4.2

Pull terms out from under the radical.

$y = \pm 2 \sqrt{6}$

Step 8.5

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

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Step 8.5.1

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

$y = 2 \sqrt{6}$

Step 8.5.2

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

$y = - 2 \sqrt{6}$

Step 8.5.3

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

$y = 2 \sqrt{6}, - 2 \sqrt{6}$

Step 9

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

${(2)}^{2} + y^{2} = 25$

Step 10

Solve the equation for $y$ .

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Step 10.1

Raise $2$ to the power of $2$ .

$4 + y^{2} = 25$

Step 10.2

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

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Step 10.2.1

Subtract $4$ from both sides of the equation.

$y^{2} = 25 - 4$

Step 10.2.2

Subtract $4$ from $25$ .

$y^{2} = 21$

Step 10.3

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

$y = \pm \sqrt{21}$

Step 10.4

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

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Step 10.4.1

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

$y = \sqrt{21}$

Step 10.4.2

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

$y = - \sqrt{21}$

Step 10.4.3

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

$y = \sqrt{21}, - \sqrt{21}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \sqrt{21} \\ - 1 & - \sqrt{21} \\ 0 & 2 \sqrt{6} \\ 1 & - 2 \sqrt{6} \\ 2 & 5 \end{array}$

Step 12