(2x)(x-2)=136

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Solution for (2x)(x-2)=136 equation: 


Simplifying
(2x)(x + -2) = 136

Remove parenthesis around (2x)
2x(x + -2) = 136

Reorder the terms:
2x(-2 + x) = 136
(-2 * 2x + x * 2x) = 136
(-4x + 2x2) = 136

Solving
-4x + 2x2 = 136

Solving for variable 'x'.

Reorder the terms:
-136 + -4x + 2x2 = 136 + -136

Combine like terms: 136 + -136 = 0
-136 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-68 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-68 + -2x + x2 = 0

Solving
-68 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '68' to each side of the equation.
-68 + -2x + 68 + x2 = 0 + 68

Reorder the terms:
-68 + 68 + -2x + x2 = 0 + 68

Combine like terms: -68 + 68 = 0
0 + -2x + x2 = 0 + 68
-2x + x2 = 0 + 68

Combine like terms: 0 + 68 = 68
-2x + x2 = 68

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 68 + 1

Reorder the terms:
1 + -2x + x2 = 68 + 1

Combine like terms: 68 + 1 = 69
1 + -2x + x2 = 69

Factor a perfect square on the left side:
(x + -1)(x + -1) = 69

Calculate the square root of the right side: 8.306623863

Break this problem into two subproblems by setting 
(x + -1) equal to 8.306623863 and -8.306623863.


Subproblem 1
x + -1 = 8.306623863

Simplifying
x + -1 = 8.306623863

Reorder the terms:
-1 + x = 8.306623863

Solving
-1 + x = 8.306623863

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 8.306623863 + 1

Combine like terms: -1 + 1 = 0
0 + x = 8.306623863 + 1
x = 8.306623863 + 1

Combine like terms: 8.306623863 + 1 = 9.306623863
x = 9.306623863

Simplifying
x = 9.306623863


Subproblem 2
x + -1 = -8.306623863

Simplifying
x + -1 = -8.306623863

Reorder the terms:
-1 + x = -8.306623863

Solving
-1 + x = -8.306623863

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -8.306623863 + 1

Combine like terms: -1 + 1 = 0
0 + x = -8.306623863 + 1
x = -8.306623863 + 1

Combine like terms: -8.306623863 + 1 = -7.306623863
x = -7.306623863

Simplifying
x = -7.306623863


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.306623863, -7.306623863}
Solution
x = {9.306623863, -7.306623863}

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