Find the Roots (Zeros) f(x)=(x-6)^2-12.25

$f (x) = {(x - 6)}^{2} - 12.25$

Step 1

Set ${(x - 6)}^{2} - 12.25$ equal to $0$ .

${(x - 6)}^{2} - 12.25 = 0$

Step 2

Solve for $x$ .

Add $12.25$ to both sides of the equation.

${(x - 6)}^{2} = 12.25$

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

$x - 6 = \pm \sqrt{12.25}$

Simplify $\pm \sqrt{12.25}$ .

Rewrite $12.25$ as ${3.5}^{2}$ .

$x - 6 = \pm \sqrt{{3.5}^{2}}$

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

$x - 6 = \pm 3.5$

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

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

$x - 6 = 3.5$

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

Add $6$ to both sides of the equation.

$x = 3.5 + 6$

Add $3.5$ and $6$ .

$x = 9.5$

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

$x - 6 = - 3.5$

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

Add $6$ to both sides of the equation.

$x = - 3.5 + 6$

Add $- 3.5$ and $6$ .

$x = 2.5$

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

$x = 9.5, 2.5$

Step 3