-2x(x-8)=26

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Solution for -2x(x-8)=26 equation: 


Simplifying
-2x(x + -8) = 26

Reorder the terms:
-2x(-8 + x) = 26
(-8 * -2x + x * -2x) = 26
(16x + -2x2) = 26

Solving
16x + -2x2 = 26

Solving for variable 'x'.

Reorder the terms:
-26 + 16x + -2x2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-13 + 8x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-13 + 8x + -1x2)' equal to zero and attempt to solve:

Simplifying
-13 + 8x + -1x2 = 0

Solving
-13 + 8x + -1x2 = 0

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

Divide each side by '-1'.
13 + -8x + x2 = 0

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + -8x + -13 + x2 = 0 + -13

Reorder the terms:
13 + -13 + -8x + x2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -8x + x2 = 0 + -13
-8x + x2 = 0 + -13

Combine like terms: 0 + -13 = -13
-8x + x2 = -13

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 = -13 + 16

Reorder the terms:
16 + -8x + x2 = -13 + 16

Combine like terms: -13 + 16 = 3
16 + -8x + x2 = 3

Factor a perfect square on the left side:
(x + -4)(x + -4) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + -4) equal to 1.732050808 and -1.732050808.


Subproblem 1
x + -4 = 1.732050808

Simplifying
x + -4 = 1.732050808

Reorder the terms:
-4 + x = 1.732050808

Solving
-4 + x = 1.732050808

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 = 1.732050808 + 4

Combine like terms: -4 + 4 = 0
0 + x = 1.732050808 + 4
x = 1.732050808 + 4

Combine like terms: 1.732050808 + 4 = 5.732050808
x = 5.732050808

Simplifying
x = 5.732050808


Subproblem 2
x + -4 = -1.732050808

Simplifying
x + -4 = -1.732050808

Reorder the terms:
-4 + x = -1.732050808

Solving
-4 + x = -1.732050808

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 = -1.732050808 + 4

Combine like terms: -4 + 4 = 0
0 + x = -1.732050808 + 4
x = -1.732050808 + 4

Combine like terms: -1.732050808 + 4 = 2.267949192
x = 2.267949192

Simplifying
x = 2.267949192


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.732050808, 2.267949192}
Solution
x = {5.732050808, 2.267949192}

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