3x^2+16x-264=0

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Solution for 3x^2+16x-264=0 equation: 


Simplifying
3x2 + 16x + -264 = 0

Reorder the terms:
-264 + 16x + 3x2 = 0

Solving
-264 + 16x + 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'.
-88 + 5.333333333x + x2 = 0

Move the constant term to the right:

Add '88' to each side of the equation.
-88 + 5.333333333x + 88 + x2 = 0 + 88

Reorder the terms:
-88 + 88 + 5.333333333x + x2 = 0 + 88

Combine like terms: -88 + 88 = 0
0 + 5.333333333x + x2 = 0 + 88
5.333333333x + x2 = 0 + 88

Combine like terms: 0 + 88 = 88
5.333333333x + x2 = 88

The x term is 5.333333333x.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333x + 7.111111113 + x2 = 88 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333x + x2 = 88 + 7.111111113

Combine like terms: 88 + 7.111111113 = 95.111111113
7.111111113 + 5.333333333x + x2 = 95.111111113

Factor a perfect square on the left side:
(x + 2.666666667)(x + 2.666666667) = 95.111111113

Calculate the square root of the right side: 9.752492559

Break this problem into two subproblems by setting 
(x + 2.666666667) equal to 9.752492559 and -9.752492559.


Subproblem 1
x + 2.666666667 = 9.752492559

Simplifying
x + 2.666666667 = 9.752492559

Reorder the terms:
2.666666667 + x = 9.752492559

Solving
2.666666667 + x = 9.752492559

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = 9.752492559 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = 9.752492559 + -2.666666667
x = 9.752492559 + -2.666666667

Combine like terms: 9.752492559 + -2.666666667 = 7.085825892
x = 7.085825892

Simplifying
x = 7.085825892


Subproblem 2
x + 2.666666667 = -9.752492559

Simplifying
x + 2.666666667 = -9.752492559

Reorder the terms:
2.666666667 + x = -9.752492559

Solving
2.666666667 + x = -9.752492559

Solving for variable 'x'.

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

Add '-2.666666667' to each side of the equation.
2.666666667 + -2.666666667 + x = -9.752492559 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + x = -9.752492559 + -2.666666667
x = -9.752492559 + -2.666666667

Combine like terms: -9.752492559 + -2.666666667 = -12.419159226
x = -12.419159226

Simplifying
x = -12.419159226


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.085825892, -12.419159226}

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