x^2-5x-8=4x+4

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Solution for x^2-5x-8=4x+4 equation: 


Simplifying
x2 + -5x + -8 = 4x + 4

Reorder the terms:
-8 + -5x + x2 = 4x + 4

Reorder the terms:
-8 + -5x + x2 = 4 + 4x

Solving
-8 + -5x + x2 = 4 + 4x

Solving for variable 'x'.

Reorder the terms:
-8 + -4 + -5x + -4x + x2 = 4 + 4x + -4 + -4x

Combine like terms: -8 + -4 = -12
-12 + -5x + -4x + x2 = 4 + 4x + -4 + -4x

Combine like terms: -5x + -4x = -9x
-12 + -9x + x2 = 4 + 4x + -4 + -4x

Reorder the terms:
-12 + -9x + x2 = 4 + -4 + 4x + -4x

Combine like terms: 4 + -4 = 0
-12 + -9x + x2 = 0 + 4x + -4x
-12 + -9x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-12 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '12' to each side of the equation.
-12 + -9x + 12 + x2 = 0 + 12

Reorder the terms:
-12 + 12 + -9x + x2 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -9x + x2 = 0 + 12
-9x + x2 = 0 + 12

Combine like terms: 0 + 12 = 12
-9x + x2 = 12

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 12 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 12 + 20.25

Combine like terms: 12 + 20.25 = 32.25
20.25 + -9x + x2 = 32.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
x + -4.5 = 5.678908346

Simplifying
x + -4.5 = 5.678908346

Reorder the terms:
-4.5 + x = 5.678908346

Solving
-4.5 + x = 5.678908346

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 5.678908346 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 5.678908346 + 4.5
x = 5.678908346 + 4.5

Combine like terms: 5.678908346 + 4.5 = 10.178908346
x = 10.178908346

Simplifying
x = 10.178908346


Subproblem 2
x + -4.5 = -5.678908346

Simplifying
x + -4.5 = -5.678908346

Reorder the terms:
-4.5 + x = -5.678908346

Solving
-4.5 + x = -5.678908346

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -5.678908346 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -5.678908346 + 4.5
x = -5.678908346 + 4.5

Combine like terms: -5.678908346 + 4.5 = -1.178908346
x = -1.178908346

Simplifying
x = -1.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.178908346, -1.178908346}

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