2x(2x-10)=134

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Solution for 2x(2x-10)=134 equation: 


Simplifying
2x(2x + -10) = 134

Reorder the terms:
2x(-10 + 2x) = 134
(-10 * 2x + 2x * 2x) = 134
(-20x + 4x2) = 134

Solving
-20x + 4x2 = 134

Solving for variable 'x'.

Reorder the terms:
-134 + -20x + 4x2 = 134 + -134

Combine like terms: 134 + -134 = 0
-134 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-67 + -10x + 2x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-67 + -10x + 2x2)' equal to zero and attempt to solve:

Simplifying
-67 + -10x + 2x2 = 0

Solving
-67 + -10x + 2x2 = 0

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

Divide each side by '2'.
-33.5 + -5x + x2 = 0

Move the constant term to the right:

Add '33.5' to each side of the equation.
-33.5 + -5x + 33.5 + x2 = 0 + 33.5

Reorder the terms:
-33.5 + 33.5 + -5x + x2 = 0 + 33.5

Combine like terms: -33.5 + 33.5 = 0.0
0.0 + -5x + x2 = 0 + 33.5
-5x + x2 = 0 + 33.5

Combine like terms: 0 + 33.5 = 33.5
-5x + x2 = 33.5

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 33.5 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 33.5 + 6.25

Combine like terms: 33.5 + 6.25 = 39.75
6.25 + -5x + x2 = 39.75

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 39.75

Calculate the square root of the right side: 6.304760106

Break this problem into two subproblems by setting 
(x + -2.5) equal to 6.304760106 and -6.304760106.


Subproblem 1
x + -2.5 = 6.304760106

Simplifying
x + -2.5 = 6.304760106

Reorder the terms:
-2.5 + x = 6.304760106

Solving
-2.5 + x = 6.304760106

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 6.304760106 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 6.304760106 + 2.5
x = 6.304760106 + 2.5

Combine like terms: 6.304760106 + 2.5 = 8.804760106
x = 8.804760106

Simplifying
x = 8.804760106


Subproblem 2
x + -2.5 = -6.304760106

Simplifying
x + -2.5 = -6.304760106

Reorder the terms:
-2.5 + x = -6.304760106

Solving
-2.5 + x = -6.304760106

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -6.304760106 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -6.304760106 + 2.5
x = -6.304760106 + 2.5

Combine like terms: -6.304760106 + 2.5 = -3.804760106
x = -3.804760106

Simplifying
x = -3.804760106


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.804760106, -3.804760106}
Solution
x = {8.804760106, -3.804760106}

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