Pre-Algebra Examples

$15^{2} + x^{2} = 25^{2}$

Step 1

Raise $15$ to the power of $2$ .

$225 + x^{2} = 25^{2}$

Step 2

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

$225 + x^{2} = 625$

Step 3

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

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Step 3.1

Subtract $225$ from both sides of the equation.

$x^{2} = 625 - 225$

Step 3.2

Subtract $225$ from $625$ .

$x^{2} = 400$

Step 4

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

$x = \pm \sqrt{400}$

Step 5

Simplify $\pm \sqrt{400}$ .

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Step 5.1

Rewrite $400$ as $20^{2}$ .

$x = \pm \sqrt{20^{2}}$

Step 5.2

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

$x = \pm 20$

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.

$x = 20$

Step 6.2

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

$x = - 20$

Step 6.3

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

$x = 20, - 20$