15x^2-67x-72=0

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Solution for 15x^2-67x-72=0 equation: 


Simplifying
15x2 + -67x + -72 = 0

Reorder the terms:
-72 + -67x + 15x2 = 0

Solving
-72 + -67x + 15x2 = 0

Solving for variable 'x'.

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

Divide each side by '15'.
-4.8 + -4.466666667x + x2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + -4.466666667x + 4.8 + x2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + -4.466666667x + x2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + -4.466666667x + x2 = 0 + 4.8
-4.466666667x + x2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
-4.466666667x + x2 = 4.8

The x term is -4.466666667x.  Take half its coefficient (-2.233333334).
Square it (4.987777781) and add it to both sides.

Add '4.987777781' to each side of the equation.
-4.466666667x + 4.987777781 + x2 = 4.8 + 4.987777781

Reorder the terms:
4.987777781 + -4.466666667x + x2 = 4.8 + 4.987777781

Combine like terms: 4.8 + 4.987777781 = 9.787777781
4.987777781 + -4.466666667x + x2 = 9.787777781

Factor a perfect square on the left side:
(x + -2.233333334)(x + -2.233333334) = 9.787777781

Calculate the square root of the right side: 3.128542437

Break this problem into two subproblems by setting 
(x + -2.233333334) equal to 3.128542437 and -3.128542437.


Subproblem 1
x + -2.233333334 = 3.128542437

Simplifying
x + -2.233333334 = 3.128542437

Reorder the terms:
-2.233333334 + x = 3.128542437

Solving
-2.233333334 + x = 3.128542437

Solving for variable 'x'.

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

Add '2.233333334' to each side of the equation.
-2.233333334 + 2.233333334 + x = 3.128542437 + 2.233333334

Combine like terms: -2.233333334 + 2.233333334 = 0.000000000
0.000000000 + x = 3.128542437 + 2.233333334
x = 3.128542437 + 2.233333334

Combine like terms: 3.128542437 + 2.233333334 = 5.361875771
x = 5.361875771

Simplifying
x = 5.361875771


Subproblem 2
x + -2.233333334 = -3.128542437

Simplifying
x + -2.233333334 = -3.128542437

Reorder the terms:
-2.233333334 + x = -3.128542437

Solving
-2.233333334 + x = -3.128542437

Solving for variable 'x'.

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

Add '2.233333334' to each side of the equation.
-2.233333334 + 2.233333334 + x = -3.128542437 + 2.233333334

Combine like terms: -2.233333334 + 2.233333334 = 0.000000000
0.000000000 + x = -3.128542437 + 2.233333334
x = -3.128542437 + 2.233333334

Combine like terms: -3.128542437 + 2.233333334 = -0.895209103
x = -0.895209103

Simplifying
x = -0.895209103


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.361875771, -0.895209103}

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