# Solve Using the Square Root Property x^2-6x-2=2

x2-6x-2=2
Move all terms to the left side of the equation and simplify.
Move 2 to the left side of the equation by subtracting it from both sides.
x2-6x-2-2=0
Subtract 2 from -2.
x2-6x-4=0
x2-6x-4=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=1, b=-6, and c=-4 into the quadratic formula and solve for x.
6±(-6)2-4⋅(1⋅-4)2⋅1
Simplify.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅-4)2⋅1
Multiply -4 by 1.
x=6±36-4⋅-42⋅1
Multiply -4 by -4.
x=6±36+162⋅1
x=6±522⋅1
Rewrite 52 as 22⋅13.
Factor 4 out of 52.
x=6±4(13)2⋅1
Rewrite 4 as 22.
x=6±22⋅132⋅1
x=6±22⋅132⋅1
Pull terms out from under the radical.
x=6±2132⋅1
x=6±2132⋅1
Multiply 2 by 1.
x=6±2132
Simplify 6±2132.
x=3±13
x=3±13
Simplify the expression to solve for the + portion of the ±.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅-4)2⋅1
Multiply -4 by 1.
x=6±36-4⋅-42⋅1
Multiply -4 by -4.
x=6±36+162⋅1
x=6±522⋅1
Rewrite 52 as 22⋅13.
Factor 4 out of 52.
x=6±4(13)2⋅1
Rewrite 4 as 22.
x=6±22⋅132⋅1
x=6±22⋅132⋅1
Pull terms out from under the radical.
x=6±2132⋅1
x=6±2132⋅1
Multiply 2 by 1.
x=6±2132
Simplify 6±2132.
x=3±13
Change the ± to +.
x=3+13
x=3+13
Simplify the expression to solve for the – portion of the ±.
Simplify the numerator.
Raise -6 to the power of 2.
x=6±36-4⋅(1⋅-4)2⋅1
Multiply -4 by 1.
x=6±36-4⋅-42⋅1
Multiply -4 by -4.
x=6±36+162⋅1
x=6±522⋅1
Rewrite 52 as 22⋅13.
Factor 4 out of 52.
x=6±4(13)2⋅1
Rewrite 4 as 22.
x=6±22⋅132⋅1
x=6±22⋅132⋅1
Pull terms out from under the radical.
x=6±2132⋅1
x=6±2132⋅1
Multiply 2 by 1.
x=6±2132
Simplify 6±2132.
x=3±13
Change the ± to -.
x=3-13
x=3-13
The final answer is the combination of both solutions.
x=3+13,3-13
The result can be shown in multiple forms.
Exact Form:
x=3+13,3-13
Decimal Form:
x=6.60555127…,-0.60555127…
Solve Using the Square Root Property x^2-6x-2=2