Find the Roots (Zeros) f(r)=(r-14)^2-56.25

$f (r) = {(r - 14)}^{2} - 56.25$

Step 1

Set ${(r - 14)}^{2} - 56.25$ equal to $0$ .

${(r - 14)}^{2} - 56.25 = 0$

Step 2

Solve for $x$ .

Add $56.25$ to both sides of the equation.

${(r - 14)}^{2} = 56.25$

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

$r - 14 = \pm \sqrt{56.25}$

Simplify $\pm \sqrt{56.25}$ .

Rewrite $56.25$ as ${7.5}^{2}$ .

$r - 14 = \pm \sqrt{{7.5}^{2}}$

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

$r - 14 = \pm 7.5$

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.

$r - 14 = 7.5$

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

Add $14$ to both sides of the equation.

$r = 7.5 + 14$

Add $7.5$ and $14$ .

$r = 21.5$

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

$r - 14 = - 7.5$

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

Add $14$ to both sides of the equation.

$r = - 7.5 + 14$

Add $- 7.5$ and $14$ .

$r = 6.5$

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

$r = 21.5, 6.5$

Step 3