# Solve Using the Square Root Property (x-2)^2-75=0 (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
Simplify the right side of the equation.
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
The complete solution is the result of both the positive and negative portions of the solution.
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     