12=6x+x2

Rewrite the equation as 6x+x2=12.

6x+x2=12

Move 12 to the left side of the equation by subtracting it from both sides.

6x+x2-12=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=6, and c=-12 into the quadratic formula and solve for x.

-6±62-4⋅(1⋅-12)2⋅1

Simplify the numerator.

Raise 6 to the power of 2.

x=-6±36-4⋅(1⋅-12)2⋅1

Multiply -12 by 1.

x=-6±36-4⋅-122⋅1

Multiply -4 by -12.

x=-6±36+482⋅1

Add 36 and 48.

x=-6±842⋅1

Rewrite 84 as 22⋅21.

Factor 4 out of 84.

x=-6±4(21)2⋅1

Rewrite 4 as 22.

x=-6±22⋅212⋅1

x=-6±22⋅212⋅1

Pull terms out from under the radical.

x=-6±2212⋅1

x=-6±2212⋅1

Multiply 2 by 1.

x=-6±2212

Simplify -6±2212.

x=-3±21

x=-3±21

Simplify the numerator.

Raise 6 to the power of 2.

x=-6±36-4⋅(1⋅-12)2⋅1

Multiply -12 by 1.

x=-6±36-4⋅-122⋅1

Multiply -4 by -12.

x=-6±36+482⋅1

Add 36 and 48.

x=-6±842⋅1

Rewrite 84 as 22⋅21.

Factor 4 out of 84.

x=-6±4(21)2⋅1

Rewrite 4 as 22.

x=-6±22⋅212⋅1

x=-6±22⋅212⋅1

Pull terms out from under the radical.

x=-6±2212⋅1

x=-6±2212⋅1

Multiply 2 by 1.

x=-6±2212

Simplify -6±2212.

x=-3±21

Change the ± to +.

x=-3+21

x=-3+21

Simplify the numerator.

Raise 6 to the power of 2.

x=-6±36-4⋅(1⋅-12)2⋅1

Multiply -12 by 1.

x=-6±36-4⋅-122⋅1

Multiply -4 by -12.

x=-6±36+482⋅1

Add 36 and 48.

x=-6±842⋅1

Rewrite 84 as 22⋅21.

Factor 4 out of 84.

x=-6±4(21)2⋅1

Rewrite 4 as 22.

x=-6±22⋅212⋅1

x=-6±22⋅212⋅1

Pull terms out from under the radical.

x=-6±2212⋅1

x=-6±2212⋅1

Multiply 2 by 1.

x=-6±2212

Simplify -6±2212.

x=-3±21

Change the ± to -.

x=-3-21

x=-3-21

The final answer is the combination of both solutions.

x=-3+21,-3-21

The result can be shown in multiple forms.

Exact Form:

x=-3+21,-3-21

Decimal Form:

x=1.58257569…,-7.58257569…

Solve Using the Square Root Property 12=6x+x^2