72x^2-2496x-936=0

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Solution for 72x^2-2496x-936=0 equation:


Simplifying
72x2 + -2496x + -936 = 0

Reorder the terms:
-936 + -2496x + 72x2 = 0

Solving
-936 + -2496x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(-39 + -104x + 3x2) = 0

Ignore the factor 24.

Subproblem 1
Set the factor '(-39 + -104x + 3x2)' equal to zero and attempt to solve:

Simplifying
-39 + -104x + 3x2 = 0

Solving
-39 + -104x + 3x2 = 0

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

Divide each side by '3'.
-13 + -34.66666667x + x2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -34.66666667x + 13 + x2 = 0 + 13

Reorder the terms:
-13 + 13 + -34.66666667x + x2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -34.66666667x + x2 = 0 + 13
-34.66666667x + x2 = 0 + 13

Combine like terms: 0 + 13 = 13
-34.66666667x + x2 = 13

The x term is -34.66666667x.  Take half its coefficient (-17.33333334).
Square it (300.4444447) and add it to both sides.

Add '300.4444447' to each side of the equation.
-34.66666667x + 300.4444447 + x2 = 13 + 300.4444447

Reorder the terms:
300.4444447 + -34.66666667x + x2 = 13 + 300.4444447

Combine like terms: 13 + 300.4444447 = 313.4444447
300.4444447 + -34.66666667x + x2 = 313.4444447

Factor a perfect square on the left side:
(x + -17.33333334)(x + -17.33333334) = 313.4444447

Calculate the square root of the right side: 17.704362307

Break this problem into two subproblems by setting 
(x + -17.33333334) equal to 17.704362307 and -17.704362307.


Subproblem 1
x + -17.33333334 = 17.704362307

Simplifying
x + -17.33333334 = 17.704362307

Reorder the terms:
-17.33333334 + x = 17.704362307

Solving
-17.33333334 + x = 17.704362307

Solving for variable 'x'.

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

Add '17.33333334' to each side of the equation.
-17.33333334 + 17.33333334 + x = 17.704362307 + 17.33333334

Combine like terms: -17.33333334 + 17.33333334 = 0.00000000
0.00000000 + x = 17.704362307 + 17.33333334
x = 17.704362307 + 17.33333334

Combine like terms: 17.704362307 + 17.33333334 = 35.037695647
x = 35.037695647

Simplifying
x = 35.037695647


Subproblem 2
x + -17.33333334 = -17.704362307

Simplifying
x + -17.33333334 = -17.704362307

Reorder the terms:
-17.33333334 + x = -17.704362307

Solving
-17.33333334 + x = -17.704362307

Solving for variable 'x'.

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

Add '17.33333334' to each side of the equation.
-17.33333334 + 17.33333334 + x = -17.704362307 + 17.33333334

Combine like terms: -17.33333334 + 17.33333334 = 0.00000000
0.00000000 + x = -17.704362307 + 17.33333334
x = -17.704362307 + 17.33333334

Combine like terms: -17.704362307 + 17.33333334 = -0.371028967
x = -0.371028967

Simplifying
x = -0.371028967


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.037695647, -0.371028967}
Solution
x = {35.037695647, -0.371028967}

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