Solve Using the Square Root Property (y-20)^2=81

${(y - 20)}^{2} = 81$

Step 1

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

$y - 20 = \pm \sqrt{81}$

Step 2

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$y - 20 = \pm \sqrt{9^{2}}$

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

$y - 20 = \pm 9$

Step 3

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.

$y - 20 = 9$

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

Add $20$ to both sides of the equation.

$y = 9 + 20$

Add $9$ and $20$ .

$y = 29$

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

$y - 20 = - 9$

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

Add $20$ to both sides of the equation.

$y = - 9 + 20$

Add $- 9$ and $20$ .

$y = 11$

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

$y = 29, 11$