Pre-Algebra Examples

8^{2} + 6^{2} = x^{2}

$8^{2} + 6^{2} = x^{2}$

Step 1

Rewrite the equation as

x^{2} = 8^{2} + 6^{2}

$x^{2} = 8^{2} + 6^{2}$ .

x^{2} = 8^{2} + 6^{2}

$x^{2} = 8^{2} + 6^{2}$

Step 2

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

x = \pm \sqrt{8^{2} + 6^{2}}

$x = \pm \sqrt{8^{2} + 6^{2}}$

Step 3

Simplify

\pm \sqrt{8^{2} + 6^{2}}

$\pm \sqrt{8^{2} + 6^{2}}$ .

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Step 3.1

Raise

8

$8$ to the power of

2

$2$ .

x = \pm \sqrt{64 + 6^{2}}

$x = \pm \sqrt{64 + 6^{2}}$

Step 3.2

Raise

6

$6$ to the power of

2

$2$ .

x = \pm \sqrt{64 + 36}

$x = \pm \sqrt{64 + 36}$

Step 3.3

Add

64

$64$ and

36

$36$ .

x = \pm \sqrt{100}

$x = \pm \sqrt{100}$

Step 3.4

Rewrite

100

$100$ as

10^{2}

$10^{2}$ .

x = \pm \sqrt{10^{2}}

$x = \pm \sqrt{10^{2}}$

Step 3.5

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

x = \pm 10

$x = \pm 10$

x = \pm 10

$x = \pm 10$

Step 4

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

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Step 4.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

x = 10

$x = 10$

Step 4.2

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

x = - 10

$x = - 10$

Step 4.3

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

x = 10, - 10

$x = 10, - 10$

x = 10, - 10

$x = 10, - 10$

8^{2} + 6^{2} = x^{2}

$8^{2} + 6^{2} = x^{2}$

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