3x^2-x-72=0

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Solution for 3x^2-x-72=0 equation: 


Simplifying
3x2 + -1x + -72 = 0

Reorder the terms:
-72 + -1x + 3x2 = 0

Solving
-72 + -1x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-24 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + -0.3333333333x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + -0.3333333333x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -0.3333333333x + x2 = 0 + 24
-0.3333333333x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
-0.3333333333x + x2 = 24

The x term is -0.3333333333x.  Take half its coefficient (-0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
-0.3333333333x + 0.02777777779 + x2 = 24 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333x + x2 = 24 + 0.02777777779

Combine like terms: 24 + 0.02777777779 = 24.02777777779
0.02777777779 + -0.3333333333x + x2 = 24.02777777779

Factor a perfect square on the left side:
(x + -0.1666666667)(x + -0.1666666667) = 24.02777777779

Calculate the square root of the right side: 4.901813723

Break this problem into two subproblems by setting 
(x + -0.1666666667) equal to 4.901813723 and -4.901813723.


Subproblem 1
x + -0.1666666667 = 4.901813723

Simplifying
x + -0.1666666667 = 4.901813723

Reorder the terms:
-0.1666666667 + x = 4.901813723

Solving
-0.1666666667 + x = 4.901813723

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = 4.901813723 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = 4.901813723 + 0.1666666667
x = 4.901813723 + 0.1666666667

Combine like terms: 4.901813723 + 0.1666666667 = 5.0684803897
x = 5.0684803897

Simplifying
x = 5.0684803897


Subproblem 2
x + -0.1666666667 = -4.901813723

Simplifying
x + -0.1666666667 = -4.901813723

Reorder the terms:
-0.1666666667 + x = -4.901813723

Solving
-0.1666666667 + x = -4.901813723

Solving for variable 'x'.

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

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 0.1666666667 + x = -4.901813723 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + x = -4.901813723 + 0.1666666667
x = -4.901813723 + 0.1666666667

Combine like terms: -4.901813723 + 0.1666666667 = -4.7351470563
x = -4.7351470563

Simplifying
x = -4.7351470563


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.0684803897, -4.7351470563}

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