2x(x-13)=144

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Solution for 2x(x-13)=144 equation: 


Simplifying
2x(x + -13) = 144

Reorder the terms:
2x(-13 + x) = 144
(-13 * 2x + x * 2x) = 144
(-26x + 2x2) = 144

Solving
-26x + 2x2 = 144

Solving for variable 'x'.

Reorder the terms:
-144 + -26x + 2x2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + -26x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-72 + -13x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-72 + -13x + x2)' equal to zero and attempt to solve:

Simplifying
-72 + -13x + x2 = 0

Solving
-72 + -13x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -13x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + -13x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -13x + x2 = 0 + 72
-13x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
-13x + x2 = 72

The x term is -13x.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13x + 42.25 + x2 = 72 + 42.25

Reorder the terms:
42.25 + -13x + x2 = 72 + 42.25

Combine like terms: 72 + 42.25 = 114.25
42.25 + -13x + x2 = 114.25

Factor a perfect square on the left side:
(x + -6.5)(x + -6.5) = 114.25

Calculate the square root of the right side: 10.688779163

Break this problem into two subproblems by setting 
(x + -6.5) equal to 10.688779163 and -10.688779163.


Subproblem 1
x + -6.5 = 10.688779163

Simplifying
x + -6.5 = 10.688779163

Reorder the terms:
-6.5 + x = 10.688779163

Solving
-6.5 + x = 10.688779163

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = 10.688779163 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = 10.688779163 + 6.5
x = 10.688779163 + 6.5

Combine like terms: 10.688779163 + 6.5 = 17.188779163
x = 17.188779163

Simplifying
x = 17.188779163


Subproblem 2
x + -6.5 = -10.688779163

Simplifying
x + -6.5 = -10.688779163

Reorder the terms:
-6.5 + x = -10.688779163

Solving
-6.5 + x = -10.688779163

Solving for variable 'x'.

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

Add '6.5' to each side of the equation.
-6.5 + 6.5 + x = -10.688779163 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + x = -10.688779163 + 6.5
x = -10.688779163 + 6.5

Combine like terms: -10.688779163 + 6.5 = -4.188779163
x = -4.188779163

Simplifying
x = -4.188779163


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.188779163, -4.188779163}
Solution
x = {17.188779163, -4.188779163}

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