(2x-8)(2x-8)=44

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Solution for (2x-8)(2x-8)=44 equation: 


Simplifying
(2x + -8)(2x + -8) = 44

Reorder the terms:
(-8 + 2x)(2x + -8) = 44

Reorder the terms:
(-8 + 2x)(-8 + 2x) = 44

Multiply (-8 + 2x) * (-8 + 2x)
(-8(-8 + 2x) + 2x * (-8 + 2x)) = 44
((-8 * -8 + 2x * -8) + 2x * (-8 + 2x)) = 44
((64 + -16x) + 2x * (-8 + 2x)) = 44
(64 + -16x + (-8 * 2x + 2x * 2x)) = 44
(64 + -16x + (-16x + 4x2)) = 44

Combine like terms: -16x + -16x = -32x
(64 + -32x + 4x2) = 44

Solving
64 + -32x + 4x2 = 44

Solving for variable 'x'.

Reorder the terms:
64 + -44 + -32x + 4x2 = 44 + -44

Combine like terms: 64 + -44 = 20
20 + -32x + 4x2 = 44 + -44

Combine like terms: 44 + -44 = 0
20 + -32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -8x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
5 + -8x + x2 = 0

Solving
5 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -8x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -8x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8x + x2 = 0 + -5
-8x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-8x + x2 = -5

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 = -5 + 16

Reorder the terms:
16 + -8x + x2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + -8x + x2 = 11

Factor a perfect square on the left side:
(x + -4)(x + -4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + -4) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + -4 = 3.31662479

Simplifying
x + -4 = 3.31662479

Reorder the terms:
-4 + x = 3.31662479

Solving
-4 + x = 3.31662479

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.31662479 + 4
x = 3.31662479 + 4

Combine like terms: 3.31662479 + 4 = 7.31662479
x = 7.31662479

Simplifying
x = 7.31662479


Subproblem 2
x + -4 = -3.31662479

Simplifying
x + -4 = -3.31662479

Reorder the terms:
-4 + x = -3.31662479

Solving
-4 + x = -3.31662479

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.31662479 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.31662479 + 4
x = -3.31662479 + 4

Combine like terms: -3.31662479 + 4 = 0.68337521
x = 0.68337521

Simplifying
x = 0.68337521


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.31662479, 0.68337521}
Solution
x = {7.31662479, 0.68337521}

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