12-x^2=8(x+4)

Solution for 12-x^2=8(x+4) equation:

Simplifying
12 + -1x2 = 8(x + 4)

Reorder the terms:
12 + -1x2 = 8(4 + x)
12 + -1x2 = (4 * 8 + x * 8)
12 + -1x2 = (32 + 8x)

Solving
12 + -1x2 = 32 + 8x

Solving for variable 'x'.

Reorder the terms:
12 + -32 + -8x + -1x2 = 32 + 8x + -32 + -8x

Combine like terms: 12 + -32 = -20
-20 + -8x + -1x2 = 32 + 8x + -32 + -8x

Reorder the terms:
-20 + -8x + -1x2 = 32 + -32 + 8x + -8x

Combine like terms: 32 + -32 = 0
-20 + -8x + -1x2 = 0 + 8x + -8x
-20 + -8x + -1x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-20 + -8x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 8x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(20 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
20 + 8x + x2 = 0

Solving
20 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + 8x + -20 + x2 = 0 + -20

Reorder the terms:
20 + -20 + 8x + x2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 8x + x2 = 0 + -20
8x + x2 = 0 + -20

Combine like terms: 0 + -20 = -20
8x + x2 = -20

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -20 + 16

Reorder the terms:
16 + 8x + x2 = -20 + 16

Combine like terms: -20 + 16 = -4
16 + 8x + x2 = -4

Factor a perfect square on the left side:
(x + 4)(x + 4) = -4

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.