Pre-Algebra Examples

$x^{2} + 6^{2} = 15^{2}$

Step 1

Raise $6$ to the power of $2$ .

$x^{2} + 36 = 15^{2}$

Step 2

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

$x^{2} + 36 = 225$

Step 3

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

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Step 3.1

Subtract $36$ from both sides of the equation.

$x^{2} = 225 - 36$

Step 3.2

Subtract $36$ from $225$ .

$x^{2} = 189$

Step 4

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

$x = \pm \sqrt{189}$

Step 5

Simplify $\pm \sqrt{189}$ .

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Step 5.1

Rewrite $189$ as $3^{2} \cdot 21$ .

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Step 5.1.1

Factor $9$ out of $189$ .

$x = \pm \sqrt{9 (21)}$

Step 5.1.2

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2} \cdot 21}$

Step 5.2

Pull terms out from under the radical.

$x = \pm 3 \sqrt{21}$

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.

$x = 3 \sqrt{21}$

Step 6.2

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

$x = - 3 \sqrt{21}$

Step 6.3

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

$x = 3 \sqrt{21}, - 3 \sqrt{21}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = 3 \sqrt{21}, - 3 \sqrt{21}$

Decimal Form:

$x = 13.74772708 \dots, - 13.74772708 \dots$