3x^2+52x+96=0

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Solution for 3x^2+52x+96=0 equation: 


Simplifying
3x2 + 52x + 96 = 0

Reorder the terms:
96 + 52x + 3x2 = 0

Solving
96 + 52x + 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'.
32 + 17.33333333x + x2 = 0

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + 17.33333333x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + 17.33333333x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 17.33333333x + x2 = 0 + -32
17.33333333x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
17.33333333x + x2 = -32

The x term is 17.33333333x.  Take half its coefficient (8.666666665).
Square it (75.11111108) and add it to both sides.

Add '75.11111108' to each side of the equation.
17.33333333x + 75.11111108 + x2 = -32 + 75.11111108

Reorder the terms:
75.11111108 + 17.33333333x + x2 = -32 + 75.11111108

Combine like terms: -32 + 75.11111108 = 43.11111108
75.11111108 + 17.33333333x + x2 = 43.11111108

Factor a perfect square on the left side:
(x + 8.666666665)(x + 8.666666665) = 43.11111108

Calculate the square root of the right side: 6.565905199

Break this problem into two subproblems by setting 
(x + 8.666666665) equal to 6.565905199 and -6.565905199.


Subproblem 1
x + 8.666666665 = 6.565905199

Simplifying
x + 8.666666665 = 6.565905199

Reorder the terms:
8.666666665 + x = 6.565905199

Solving
8.666666665 + x = 6.565905199

Solving for variable 'x'.

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

Add '-8.666666665' to each side of the equation.
8.666666665 + -8.666666665 + x = 6.565905199 + -8.666666665

Combine like terms: 8.666666665 + -8.666666665 = 0.000000000
0.000000000 + x = 6.565905199 + -8.666666665
x = 6.565905199 + -8.666666665

Combine like terms: 6.565905199 + -8.666666665 = -2.100761466
x = -2.100761466

Simplifying
x = -2.100761466


Subproblem 2
x + 8.666666665 = -6.565905199

Simplifying
x + 8.666666665 = -6.565905199

Reorder the terms:
8.666666665 + x = -6.565905199

Solving
8.666666665 + x = -6.565905199

Solving for variable 'x'.

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

Add '-8.666666665' to each side of the equation.
8.666666665 + -8.666666665 + x = -6.565905199 + -8.666666665

Combine like terms: 8.666666665 + -8.666666665 = 0.000000000
0.000000000 + x = -6.565905199 + -8.666666665
x = -6.565905199 + -8.666666665

Combine like terms: -6.565905199 + -8.666666665 = -15.232571864
x = -15.232571864

Simplifying
x = -15.232571864


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.100761466, -15.232571864}

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