x2+6x-6=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=6, and c=-6 into the quadratic formula and solve for x.

-6±62-4⋅(1⋅-6)2⋅1

Simplify the numerator.

Raise 6 to the power of 2.

x=-6±36-4⋅(1⋅-6)2⋅1

Multiply -6 by 1.

x=-6±36-4⋅-62⋅1

Multiply -4 by -6.

x=-6±36+242⋅1

Add 36 and 24.

x=-6±602⋅1

Rewrite 60 as 22⋅15.

Factor 4 out of 60.

x=-6±4(15)2⋅1

Rewrite 4 as 22.

x=-6±22⋅152⋅1

x=-6±22⋅152⋅1

Pull terms out from under the radical.

x=-6±2152⋅1

x=-6±2152⋅1

Multiply 2 by 1.

x=-6±2152

Simplify -6±2152.

x=-3±15

x=-3±15

Simplify the numerator.

Raise 6 to the power of 2.

x=-6±36-4⋅(1⋅-6)2⋅1

Multiply -6 by 1.

x=-6±36-4⋅-62⋅1

Multiply -4 by -6.

x=-6±36+242⋅1

Add 36 and 24.

x=-6±602⋅1

Rewrite 60 as 22⋅15.

Factor 4 out of 60.

x=-6±4(15)2⋅1

Rewrite 4 as 22.

x=-6±22⋅152⋅1

x=-6±22⋅152⋅1

Pull terms out from under the radical.

x=-6±2152⋅1

x=-6±2152⋅1

Multiply 2 by 1.

x=-6±2152

Simplify -6±2152.

x=-3±15

Change the ± to +.

x=-3+15

x=-3+15

Simplify the numerator.

Raise 6 to the power of 2.

x=-6±36-4⋅(1⋅-6)2⋅1

Multiply -6 by 1.

x=-6±36-4⋅-62⋅1

Multiply -4 by -6.

x=-6±36+242⋅1

Add 36 and 24.

x=-6±602⋅1

Rewrite 60 as 22⋅15.

Factor 4 out of 60.

x=-6±4(15)2⋅1

Rewrite 4 as 22.

x=-6±22⋅152⋅1

x=-6±22⋅152⋅1

Pull terms out from under the radical.

x=-6±2152⋅1

x=-6±2152⋅1

Multiply 2 by 1.

x=-6±2152

Simplify -6±2152.

x=-3±15

Change the ± to -.

x=-3-15

x=-3-15

The final answer is the combination of both solutions.

x=-3+15,-3-15

The result can be shown in multiple forms.

Exact Form:

x=-3+15,-3-15

Decimal Form:

x=0.87298334…,-6.87298334…

Solve Using the Square Root Property x^2+6x-6=0