Precalculus Examples

$f (x) = {(x + 2)}^{2} - 25$

Step 1

Set ${(x + 2)}^{2} - 25$ equal to $0$ .

${(x + 2)}^{2} - 25 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $25$ to both sides of the equation.

${(x + 2)}^{2} = 25$

Step 2.2

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

$x + 2 = \pm \sqrt{25}$

Step 2.3

Simplify $\pm \sqrt{25}$ .

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Step 2.3.1

Rewrite $25$ as $5^{2}$ .

$x + 2 = \pm \sqrt{5^{2}}$

Step 2.3.2

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

$x + 2 = \pm 5$

Step 2.4

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

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Step 2.4.1

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

$x + 2 = 5$

Step 2.4.2

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

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Step 2.4.2.1

Subtract $2$ from both sides of the equation.

$x = 5 - 2$

Step 2.4.2.2

Subtract $2$ from $5$ .

$x = 3$

Step 2.4.3

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

$x + 2 = - 5$

Step 2.4.4

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

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Step 2.4.4.1

Subtract $2$ from both sides of the equation.

$x = - 5 - 2$

Step 2.4.4.2

Subtract $2$ from $- 5$ .

$x = - 7$

Step 2.4.5

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

$x = 3, - 7$

Step 3