3x^2+33x-72=0

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Solution for 3x^2+33x-72=0 equation: 


Simplifying
3x2 + 33x + -72 = 0

Reorder the terms:
-72 + 33x + 3x2 = 0

Solving
-72 + 33x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 11x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-24 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
-24 + 11x + x2 = 0

Solving
-24 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '24' to each side of the equation.
-24 + 11x + 24 + x2 = 0 + 24

Reorder the terms:
-24 + 24 + 11x + x2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + 11x + x2 = 0 + 24
11x + x2 = 0 + 24

Combine like terms: 0 + 24 = 24
11x + x2 = 24

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 24 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 24 + 30.25

Combine like terms: 24 + 30.25 = 54.25
30.25 + 11x + x2 = 54.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(x + 5.5) equal to 7.365459931 and -7.365459931.


Subproblem 1
x + 5.5 = 7.365459931

Simplifying
x + 5.5 = 7.365459931

Reorder the terms:
5.5 + x = 7.365459931

Solving
5.5 + x = 7.365459931

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 7.365459931 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 7.365459931 + -5.5
x = 7.365459931 + -5.5

Combine like terms: 7.365459931 + -5.5 = 1.865459931
x = 1.865459931

Simplifying
x = 1.865459931


Subproblem 2
x + 5.5 = -7.365459931

Simplifying
x + 5.5 = -7.365459931

Reorder the terms:
5.5 + x = -7.365459931

Solving
5.5 + x = -7.365459931

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -7.365459931 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -7.365459931 + -5.5
x = -7.365459931 + -5.5

Combine like terms: -7.365459931 + -5.5 = -12.865459931
x = -12.865459931

Simplifying
x = -12.865459931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.865459931, -12.865459931}
Solution
x = {1.865459931, -12.865459931}

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