-2x(x-8)=28

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Solution for -2x(x-8)=28 equation: 


Simplifying
-2x(x + -8) = 28

Reorder the terms:
-2x(-8 + x) = 28
(-8 * -2x + x * -2x) = 28
(16x + -2x2) = 28

Solving
16x + -2x2 = 28

Solving for variable 'x'.

Reorder the terms:
-28 + 16x + -2x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-28 + 16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-14 + 8x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-14 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
-14 + 8x + -1x2 = 0

Solving
-14 + 8x + -1x2 = 0

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

Divide each side by '-1'.
14 + -8x + x2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -8x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + -8x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -8x + x2 = 0 + -14
-8x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
-8x + x2 = -14

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 = -14 + 16

Reorder the terms:
16 + -8x + x2 = -14 + 16

Combine like terms: -14 + 16 = 2
16 + -8x + x2 = 2

Factor a perfect square on the left side:
(x + -4)(x + -4) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + -4) equal to 1.414213562 and -1.414213562.


Subproblem 1
x + -4 = 1.414213562

Simplifying
x + -4 = 1.414213562

Reorder the terms:
-4 + x = 1.414213562

Solving
-4 + x = 1.414213562

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 = 1.414213562 + 4

Combine like terms: -4 + 4 = 0
0 + x = 1.414213562 + 4
x = 1.414213562 + 4

Combine like terms: 1.414213562 + 4 = 5.414213562
x = 5.414213562

Simplifying
x = 5.414213562


Subproblem 2
x + -4 = -1.414213562

Simplifying
x + -4 = -1.414213562

Reorder the terms:
-4 + x = -1.414213562

Solving
-4 + x = -1.414213562

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 = -1.414213562 + 4

Combine like terms: -4 + 4 = 0
0 + x = -1.414213562 + 4
x = -1.414213562 + 4

Combine like terms: -1.414213562 + 4 = 2.585786438
x = 2.585786438

Simplifying
x = 2.585786438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.414213562, 2.585786438}
Solution
x = {5.414213562, 2.585786438}

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