8x-4x^2=12x+32

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Solution for 8x-4x^2=12x+32 equation: 


Simplifying
8x + -4x2 = 12x + 32

Reorder the terms:
8x + -4x2 = 32 + 12x

Solving
8x + -4x2 = 32 + 12x

Solving for variable 'x'.

Reorder the terms:
-32 + 8x + -12x + -4x2 = 32 + 12x + -32 + -12x

Combine like terms: 8x + -12x = -4x
-32 + -4x + -4x2 = 32 + 12x + -32 + -12x

Reorder the terms:
-32 + -4x + -4x2 = 32 + -32 + 12x + -12x

Combine like terms: 32 + -32 = 0
-32 + -4x + -4x2 = 0 + 12x + -12x
-32 + -4x + -4x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-32 + -4x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-4'.
-4(8 + x + x2) = 0

Ignore the factor -4.

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

Simplifying
8 + x + x2 = 0

Solving
8 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = -8 + 0.25

Reorder the terms:
0.25 + x + x2 = -8 + 0.25

Combine like terms: -8 + 0.25 = -7.75
0.25 + x + x2 = -7.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -7.75

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.

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