2x(2x-16)=8

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Solution for 2x(2x-16)=8 equation: 


Simplifying
2x(2x + -16) = 8

Reorder the terms:
2x(-16 + 2x) = 8
(-16 * 2x + 2x * 2x) = 8
(-32x + 4x2) = 8

Solving
-32x + 4x2 = 8

Solving for variable 'x'.

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

Combine like terms: 8 + -8 = 0
-8 + -32x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + -8x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-2 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -8x + x2 = 0

Solving
-2 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -8x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -8x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -8x + x2 = 0 + 2
-8x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-8x + x2 = 2

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 = 2 + 16

Reorder the terms:
16 + -8x + x2 = 2 + 16

Combine like terms: 2 + 16 = 18
16 + -8x + x2 = 18

Factor a perfect square on the left side:
(x + -4)(x + -4) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -4) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + -4 = 4.242640687

Simplifying
x + -4 = 4.242640687

Reorder the terms:
-4 + x = 4.242640687

Solving
-4 + x = 4.242640687

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 = 4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.242640687 + 4
x = 4.242640687 + 4

Combine like terms: 4.242640687 + 4 = 8.242640687
x = 8.242640687

Simplifying
x = 8.242640687


Subproblem 2
x + -4 = -4.242640687

Simplifying
x + -4 = -4.242640687

Reorder the terms:
-4 + x = -4.242640687

Solving
-4 + x = -4.242640687

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 = -4.242640687 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.242640687 + 4
x = -4.242640687 + 4

Combine like terms: -4.242640687 + 4 = -0.242640687
x = -0.242640687

Simplifying
x = -0.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.242640687, -0.242640687}
Solution
x = {8.242640687, -0.242640687}

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