3x^2+44x-96=0

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Solution for 3x^2+44x-96=0 equation: 


Simplifying
3x2 + 44x + -96 = 0

Reorder the terms:
-96 + 44x + 3x2 = 0

Solving
-96 + 44x + 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 + 14.66666667x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 14.66666667x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 14.66666667x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 14.66666667x + x2 = 0 + 32
14.66666667x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
14.66666667x + x2 = 32

The x term is 14.66666667x.  Take half its coefficient (7.333333335).
Square it (53.77777780) and add it to both sides.

Add '53.77777780' to each side of the equation.
14.66666667x + 53.77777780 + x2 = 32 + 53.77777780

Reorder the terms:
53.77777780 + 14.66666667x + x2 = 32 + 53.77777780

Combine like terms: 32 + 53.77777780 = 85.7777778
53.77777780 + 14.66666667x + x2 = 85.7777778

Factor a perfect square on the left side:
(x + 7.333333335)(x + 7.333333335) = 85.7777778

Calculate the square root of the right side: 9.261629328

Break this problem into two subproblems by setting 
(x + 7.333333335) equal to 9.261629328 and -9.261629328.


Subproblem 1
x + 7.333333335 = 9.261629328

Simplifying
x + 7.333333335 = 9.261629328

Reorder the terms:
7.333333335 + x = 9.261629328

Solving
7.333333335 + x = 9.261629328

Solving for variable 'x'.

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

Add '-7.333333335' to each side of the equation.
7.333333335 + -7.333333335 + x = 9.261629328 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + x = 9.261629328 + -7.333333335
x = 9.261629328 + -7.333333335

Combine like terms: 9.261629328 + -7.333333335 = 1.928295993
x = 1.928295993

Simplifying
x = 1.928295993


Subproblem 2
x + 7.333333335 = -9.261629328

Simplifying
x + 7.333333335 = -9.261629328

Reorder the terms:
7.333333335 + x = -9.261629328

Solving
7.333333335 + x = -9.261629328

Solving for variable 'x'.

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

Add '-7.333333335' to each side of the equation.
7.333333335 + -7.333333335 + x = -9.261629328 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + x = -9.261629328 + -7.333333335
x = -9.261629328 + -7.333333335

Combine like terms: -9.261629328 + -7.333333335 = -16.594962663
x = -16.594962663

Simplifying
x = -16.594962663


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.928295993, -16.594962663}

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