Trigonometry Examples

${(x - 17)}^{2} = 12$

Step 1

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

$x - 17 = \pm \sqrt{12}$

Step 2

Simplify $\pm \sqrt{12}$ .

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Step 2.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 2.1.1

Factor $4$ out of $12$ .

$x - 17 = \pm \sqrt{4 (3)}$

Step 2.1.2

Rewrite $4$ as $2^{2}$ .

$x - 17 = \pm \sqrt{2^{2} \cdot 3}$

Step 2.2

Pull terms out from under the radical.

$x - 17 = \pm 2 \sqrt{3}$

Step 3

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

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Step 3.1

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

$x - 17 = 2 \sqrt{3}$

Step 3.2

Add $17$ to both sides of the equation.

$x = 2 \sqrt{3} + 17$

Step 3.3

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

$x - 17 = - 2 \sqrt{3}$

Step 3.4

Add $17$ to both sides of the equation.

$x = - 2 \sqrt{3} + 17$

Step 3.5

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

$x = 2 \sqrt{3} + 17, - 2 \sqrt{3} + 17$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{3} + 17, - 2 \sqrt{3} + 17$

Decimal Form:

$x = 20.46410161 \dots, 13.53589838 \dots$