Solve Using the Square Root Property (X-3)^2=64

${(X - 3)}^{2} = 64$

Step 1

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

$X - 3 = \pm \sqrt{64}$

Step 2

Simplify $\pm \sqrt{64}$ .

Rewrite $64$ as $8^{2}$ .

$X - 3 = \pm \sqrt{8^{2}}$

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

$X - 3 = \pm 8$

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.

$X - 3 = 8$

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

Add $3$ to both sides of the equation.

$X = 8 + 3$

Add $8$ and $3$ .

$X = 11$

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

$X - 3 = - 8$

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

Add $3$ to both sides of the equation.

$X = - 8 + 3$

Add $- 8$ and $3$ .

$X = - 5$

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

$X = 11, - 5$