3x^2+44x-121=0

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Solution for 3x^2+44x-121=0 equation: 


Simplifying
3x2 + 44x + -121 = 0

Reorder the terms:
-121 + 44x + 3x2 = 0

Solving
-121 + 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'.
-40.33333333 + 14.66666667x + x2 = 0

Move the constant term to the right:

Add '40.33333333' to each side of the equation.
-40.33333333 + 14.66666667x + 40.33333333 + x2 = 0 + 40.33333333

Reorder the terms:
-40.33333333 + 40.33333333 + 14.66666667x + x2 = 0 + 40.33333333

Combine like terms: -40.33333333 + 40.33333333 = 0.00000000
0.00000000 + 14.66666667x + x2 = 0 + 40.33333333
14.66666667x + x2 = 0 + 40.33333333

Combine like terms: 0 + 40.33333333 = 40.33333333
14.66666667x + x2 = 40.33333333

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 = 40.33333333 + 53.77777780

Reorder the terms:
53.77777780 + 14.66666667x + x2 = 40.33333333 + 53.77777780

Combine like terms: 40.33333333 + 53.77777780 = 94.11111113
53.77777780 + 14.66666667x + x2 = 94.11111113

Factor a perfect square on the left side:
(x + 7.333333335)(x + 7.333333335) = 94.11111113

Calculate the square root of the right side: 9.701088142

Break this problem into two subproblems by setting 
(x + 7.333333335) equal to 9.701088142 and -9.701088142.


Subproblem 1
x + 7.333333335 = 9.701088142

Simplifying
x + 7.333333335 = 9.701088142

Reorder the terms:
7.333333335 + x = 9.701088142

Solving
7.333333335 + x = 9.701088142

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 = 9.701088142 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + x = 9.701088142 + -7.333333335
x = 9.701088142 + -7.333333335

Combine like terms: 9.701088142 + -7.333333335 = 2.367754807
x = 2.367754807

Simplifying
x = 2.367754807


Subproblem 2
x + 7.333333335 = -9.701088142

Simplifying
x + 7.333333335 = -9.701088142

Reorder the terms:
7.333333335 + x = -9.701088142

Solving
7.333333335 + x = -9.701088142

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 = -9.701088142 + -7.333333335

Combine like terms: 7.333333335 + -7.333333335 = 0.000000000
0.000000000 + x = -9.701088142 + -7.333333335
x = -9.701088142 + -7.333333335

Combine like terms: -9.701088142 + -7.333333335 = -17.034421477
x = -17.034421477

Simplifying
x = -17.034421477


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.367754807, -17.034421477}

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