Precalculus Examples

$7^{2} + y^{2} = 25^{2}$

Step 1

Raise $7$ to the power of $2$ .

$49 + y^{2} = 25^{2}$

Step 2

Raise $25$ to the power of $2$ .

$49 + y^{2} = 625$

Step 3

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

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Step 3.1

Subtract $49$ from both sides of the equation.

$y^{2} = 625 - 49$

Step 3.2

Subtract $49$ from $625$ .

$y^{2} = 576$

Step 4

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

$y = \pm \sqrt{576}$

Step 5

Simplify $\pm \sqrt{576}$ .

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Step 5.1

Rewrite $576$ as $24^{2}$ .

$y = \pm \sqrt{24^{2}}$

Step 5.2

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

$y = \pm 24$

Step 6

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

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Step 6.1

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

$y = 24$

Step 6.2

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

$y = - 24$

Step 6.3

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

$y = 24, - 24$