2x^2-15x-144=0

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Solution for 2x^2-15x-144=0 equation: 


Simplifying
2x2 + -15x + -144 = 0

Reorder the terms:
-144 + -15x + 2x2 = 0

Solving
-144 + -15x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-72 + -7.5x + x2 = 0

Move the constant term to the right:

Add '72' to each side of the equation.
-72 + -7.5x + 72 + x2 = 0 + 72

Reorder the terms:
-72 + 72 + -7.5x + x2 = 0 + 72

Combine like terms: -72 + 72 = 0
0 + -7.5x + x2 = 0 + 72
-7.5x + x2 = 0 + 72

Combine like terms: 0 + 72 = 72
-7.5x + x2 = 72

The x term is -7.5x.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5x + 14.0625 + x2 = 72 + 14.0625

Reorder the terms:
14.0625 + -7.5x + x2 = 72 + 14.0625

Combine like terms: 72 + 14.0625 = 86.0625
14.0625 + -7.5x + x2 = 86.0625

Factor a perfect square on the left side:
(x + -3.75)(x + -3.75) = 86.0625

Calculate the square root of the right side: 9.276987658

Break this problem into two subproblems by setting 
(x + -3.75) equal to 9.276987658 and -9.276987658.


Subproblem 1
x + -3.75 = 9.276987658

Simplifying
x + -3.75 = 9.276987658

Reorder the terms:
-3.75 + x = 9.276987658

Solving
-3.75 + x = 9.276987658

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = 9.276987658 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = 9.276987658 + 3.75
x = 9.276987658 + 3.75

Combine like terms: 9.276987658 + 3.75 = 13.026987658
x = 13.026987658

Simplifying
x = 13.026987658


Subproblem 2
x + -3.75 = -9.276987658

Simplifying
x + -3.75 = -9.276987658

Reorder the terms:
-3.75 + x = -9.276987658

Solving
-3.75 + x = -9.276987658

Solving for variable 'x'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + x = -9.276987658 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + x = -9.276987658 + 3.75
x = -9.276987658 + 3.75

Combine like terms: -9.276987658 + 3.75 = -5.526987658
x = -5.526987658

Simplifying
x = -5.526987658


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.026987658, -5.526987658}

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