-12x^2-88x+121=0

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Solution for -12x^2-88x+121=0 equation: 


Simplifying
-12x2 + -88x + 121 = 0

Reorder the terms:
121 + -88x + -12x2 = 0

Solving
121 + -88x + -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'.
-10.08333333 + 7.333333333x + x2 = 0

Move the constant term to the right:

Add '10.08333333' to each side of the equation.
-10.08333333 + 7.333333333x + 10.08333333 + x2 = 0 + 10.08333333

Reorder the terms:
-10.08333333 + 10.08333333 + 7.333333333x + x2 = 0 + 10.08333333

Combine like terms: -10.08333333 + 10.08333333 = 0.00000000
0.00000000 + 7.333333333x + x2 = 0 + 10.08333333
7.333333333x + x2 = 0 + 10.08333333

Combine like terms: 0 + 10.08333333 = 10.08333333
7.333333333x + x2 = 10.08333333

The x term is 7.333333333x.  Take half its coefficient (3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
7.333333333x + 13.44444445 + x2 = 10.08333333 + 13.44444445

Reorder the terms:
13.44444445 + 7.333333333x + x2 = 10.08333333 + 13.44444445

Combine like terms: 10.08333333 + 13.44444445 = 23.52777778
13.44444445 + 7.333333333x + x2 = 23.52777778

Factor a perfect square on the left side:
(x + 3.666666667)(x + 3.666666667) = 23.52777778

Calculate the square root of the right side: 4.850544071

Break this problem into two subproblems by setting 
(x + 3.666666667) equal to 4.850544071 and -4.850544071.


Subproblem 1
x + 3.666666667 = 4.850544071

Simplifying
x + 3.666666667 = 4.850544071

Reorder the terms:
3.666666667 + x = 4.850544071

Solving
3.666666667 + x = 4.850544071

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = 4.850544071 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = 4.850544071 + -3.666666667
x = 4.850544071 + -3.666666667

Combine like terms: 4.850544071 + -3.666666667 = 1.183877404
x = 1.183877404

Simplifying
x = 1.183877404


Subproblem 2
x + 3.666666667 = -4.850544071

Simplifying
x + 3.666666667 = -4.850544071

Reorder the terms:
3.666666667 + x = -4.850544071

Solving
3.666666667 + x = -4.850544071

Solving for variable 'x'.

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

Add '-3.666666667' to each side of the equation.
3.666666667 + -3.666666667 + x = -4.850544071 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + x = -4.850544071 + -3.666666667
x = -4.850544071 + -3.666666667

Combine like terms: -4.850544071 + -3.666666667 = -8.517210738
x = -8.517210738

Simplifying
x = -8.517210738


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.183877404, -8.517210738}

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