12x^2+80x+91=0

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Solution for 12x^2+80x+91=0 equation: 


Simplifying
12x2 + 80x + 91 = 0

Reorder the terms:
91 + 80x + 12x2 = 0

Solving
91 + 80x + 12x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
12 the coefficient of the squared term: 

Divide each side by '12'.
7.583333333 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '-7.583333333' to each side of the equation.
7.583333333 + 6.666666667x + -7.583333333 + x2 = 0 + -7.583333333

Reorder the terms:
7.583333333 + -7.583333333 + 6.666666667x + x2 = 0 + -7.583333333

Combine like terms: 7.583333333 + -7.583333333 = 0.000000000
0.000000000 + 6.666666667x + x2 = 0 + -7.583333333
6.666666667x + x2 = 0 + -7.583333333

Combine like terms: 0 + -7.583333333 = -7.583333333
6.666666667x + x2 = -7.583333333

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = -7.583333333 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = -7.583333333 + 11.11111112

Combine like terms: -7.583333333 + 11.11111112 = 3.527777787
11.11111112 + 6.666666667x + x2 = 3.527777787

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 3.527777787

Calculate the square root of the right side: 1.878237947

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 1.878237947 and -1.878237947.


Subproblem 1
x + 3.333333334 = 1.878237947

Simplifying
x + 3.333333334 = 1.878237947

Reorder the terms:
3.333333334 + x = 1.878237947

Solving
3.333333334 + x = 1.878237947

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 1.878237947 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 1.878237947 + -3.333333334
x = 1.878237947 + -3.333333334

Combine like terms: 1.878237947 + -3.333333334 = -1.455095387
x = -1.455095387

Simplifying
x = -1.455095387


Subproblem 2
x + 3.333333334 = -1.878237947

Simplifying
x + 3.333333334 = -1.878237947

Reorder the terms:
3.333333334 + x = -1.878237947

Solving
3.333333334 + x = -1.878237947

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -1.878237947 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -1.878237947 + -3.333333334
x = -1.878237947 + -3.333333334

Combine like terms: -1.878237947 + -3.333333334 = -5.211571281
x = -5.211571281

Simplifying
x = -5.211571281


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.455095387, -5.211571281}

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