Solve Using the Square Root Property (x-2)^2=25

${(x - 2)}^{2} = 25$

Step 1

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

$x - 2 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$x - 2 = \pm \sqrt{5^{2}}$

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

$x - 2 = \pm 5$

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.

$x - 2 = 5$

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

Add $2$ to both sides of the equation.

$x = 5 + 2$

Add $5$ and $2$ .

$x = 7$

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

$x - 2 = - 5$

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

Add $2$ to both sides of the equation.

$x = - 5 + 2$

Add $- 5$ and $2$ .

$x = - 3$

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

$x = 7, - 3$