2x(5x-2)=136

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Solution for 2x(5x-2)=136 equation: 


Simplifying
2x(5x + -2) = 136

Reorder the terms:
2x(-2 + 5x) = 136
(-2 * 2x + 5x * 2x) = 136
(-4x + 10x2) = 136

Solving
-4x + 10x2 = 136

Solving for variable 'x'.

Reorder the terms:
-136 + -4x + 10x2 = 136 + -136

Combine like terms: 136 + -136 = 0
-136 + -4x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-68 + -2x + 5x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-68 + -2x + 5x2)' equal to zero and attempt to solve:

Simplifying
-68 + -2x + 5x2 = 0

Solving
-68 + -2x + 5x2 = 0

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

Divide each side by '5'.
-13.6 + -0.4x + x2 = 0

Move the constant term to the right:

Add '13.6' to each side of the equation.
-13.6 + -0.4x + 13.6 + x2 = 0 + 13.6

Reorder the terms:
-13.6 + 13.6 + -0.4x + x2 = 0 + 13.6

Combine like terms: -13.6 + 13.6 = 0.0
0.0 + -0.4x + x2 = 0 + 13.6
-0.4x + x2 = 0 + 13.6

Combine like terms: 0 + 13.6 = 13.6
-0.4x + x2 = 13.6

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 13.6 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 13.6 + 0.04

Combine like terms: 13.6 + 0.04 = 13.64
0.04 + -0.4x + x2 = 13.64

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 13.64

Calculate the square root of the right side: 3.693237063

Break this problem into two subproblems by setting 
(x + -0.2) equal to 3.693237063 and -3.693237063.


Subproblem 1
x + -0.2 = 3.693237063

Simplifying
x + -0.2 = 3.693237063

Reorder the terms:
-0.2 + x = 3.693237063

Solving
-0.2 + x = 3.693237063

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = 3.693237063 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = 3.693237063 + 0.2
x = 3.693237063 + 0.2

Combine like terms: 3.693237063 + 0.2 = 3.893237063
x = 3.893237063

Simplifying
x = 3.893237063


Subproblem 2
x + -0.2 = -3.693237063

Simplifying
x + -0.2 = -3.693237063

Reorder the terms:
-0.2 + x = -3.693237063

Solving
-0.2 + x = -3.693237063

Solving for variable 'x'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + x = -3.693237063 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + x = -3.693237063 + 0.2
x = -3.693237063 + 0.2

Combine like terms: -3.693237063 + 0.2 = -3.493237063
x = -3.493237063

Simplifying
x = -3.493237063


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.893237063, -3.493237063}
Solution
x = {3.893237063, -3.493237063}

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