Pre-Algebra Examples

$8^{2} + x^{2} = 10^{2}$

Step 1

Raise

$8$ to the power of

$2$ .

$64 + x^{2} = 10^{2}$

Step 2

Raise

$10$ to the power of

$2$ .

$64 + x^{2} = 100$

Step 3

Move all terms not containing

$x$ to the right side of the equation.

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Step 3.1

Subtract

$64$ from both sides of the equation.

$x^{2} = 100 - 64$

Step 3.2

Subtract

$64$ from

$100$ .

$x^{2} = 36$

Step 4

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

$x = \pm \sqrt{36}$

Step 5

Simplify

$\pm \sqrt{36}$ .

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Step 5.1

Rewrite

$36$ as

$6^{2}$ .

$x = \pm \sqrt{6^{2}}$

Step 5.2

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

$x = \pm 6$

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.

$x = 6$

Step 6.2

Next, use the negative value of the

$\pm$ to find the second solution.

$x = - 6$

Step 6.3

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

$x = 6, - 6$