0=4(x^2+8x-2)

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Solution for 0=4(x^2+8x-2) equation: 


Simplifying
0 = 4(x2 + 8x + -2)

Reorder the terms:
0 = 4(-2 + 8x + x2)
0 = (-2 * 4 + 8x * 4 + x2 * 4)
0 = (-8 + 32x + 4x2)

Solving
0 = -8 + 32x + 4x2

Solving for variable 'x'.

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

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

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

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(2 + -8x + -1x2) = 0

Ignore the factor 4.

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

Simplifying
2 + -8x + -1x2 = 0

Solving
2 + -8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + 8x + x2 = 0

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 = 0.242640687
x = 0.242640687

Simplifying
x = 0.242640687


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 = -8.242640687
x = -8.242640687

Simplifying
x = -8.242640687


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

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