(x-2)2-75=0

Add 75 to both sides of the equation.

(x-2)2=75

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

(x-2)2⋅12=±75

Remove the perfect root factor x-2 under the radical to solve for x.

x-2=±75

Rewrite 75 as 52⋅3.

Factor 25 out of 75.

x-2=±25(3)

Rewrite 25 as 52.

x-2=±52⋅3

x-2=±52⋅3

Pull terms out from under the radical.

x-2=±53

x-2=±53

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

x-2=53

Add 2 to both sides of the equation.

x=53+2

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

x-2=-53

Add 2 to both sides of the equation.

x=-53+2

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

x=53+2,-53+2

x=53+2,-53+2

The result can be shown in multiple forms.

Exact Form:

x=53+2,-53+2

Decimal Form:

x=10.66025403…,-6.66025403…

Solve Using the Square Root Property (x-2)^2-75=0