(x-13)2=20

Take the square root of each side of the equation to set up the solution for x

(x-13)2⋅12=±20

Remove the perfect root factor x-13 under the radical to solve for x.

x-13=±20

Rewrite 20 as 22⋅5.

Factor 4 out of 20.

x-13=±4(5)

Rewrite 4 as 22.

x-13=±22⋅5

x-13=±22⋅5

Pull terms out from under the radical.

x-13=±25

x-13=±25

First, use the positive value of the ± to find the first solution.

x-13=25

Add 13 to both sides of the equation.

x=25+13

Next, use the negative value of the ± to find the second solution.

x-13=-25

Add 13 to both sides of the equation.

x=-25+13

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

x=25+13,-25+13

x=25+13,-25+13

The result can be shown in multiple forms.

Exact Form:

x=25+13,-25+13

Decimal Form:

x=17.47213595…,8.52786404…

Solve Using the Square Root Property (x-13)^2=20