Precalculus Examples

${(x + 4)}^{2} = 144$

Step 1

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

$x + 4 = \pm \sqrt{144}$

Step 2

Simplify $\pm \sqrt{144}$ .

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Step 2.1

Rewrite $144$ as $12^{2}$ .

$x + 4 = \pm \sqrt{12^{2}}$

Step 2.2

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

$x + 4 = \pm 12$

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.

$x + 4 = 12$

Step 3.2

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

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Step 3.2.1

Subtract $4$ from both sides of the equation.

$x = 12 - 4$

Step 3.2.2

Subtract $4$ from $12$ .

$x = 8$

Step 3.3

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

$x + 4 = - 12$

Step 3.4

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

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Step 3.4.1

Subtract $4$ from both sides of the equation.

$x = - 12 - 4$

Step 3.4.2

Subtract $4$ from $- 12$ .

$x = - 16$

Step 3.5

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

$x = 8, - 16$