Precalculus Examples

$f (x) = {(x - 1)}^{2} - 9$

Step 1

Set ${(x - 1)}^{2} - 9$ equal to $0$ .

${(x - 1)}^{2} - 9 = 0$

Step 2

Solve for $x$ .

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Step 2.1

Add $9$ to both sides of the equation.

${(x - 1)}^{2} = 9$

Step 2.2

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

$x - 1 = \pm \sqrt{9}$

Step 2.3

Simplify $\pm \sqrt{9}$ .

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Step 2.3.1

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

$x - 1 = \pm \sqrt{3^{2}}$

Step 2.3.2

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

$x - 1 = \pm 3$

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.

$x - 1 = 3$

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

Add $1$ to both sides of the equation.

$x = 3 + 1$

Step 2.4.2.2

Add $3$ and $1$ .

$x = 4$

Step 2.4.3

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

$x - 1 = - 3$

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

Add $1$ to both sides of the equation.

$x = - 3 + 1$

Step 2.4.4.2

Add $- 3$ and $1$ .

$x = - 2$

Step 2.4.5

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

$x = 4, - 2$

Step 3