-12x^2-6x+7=-155

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Solution for -12x^2-6x+7=-155 equation: 


Simplifying
-12x2 + -6x + 7 = -155

Reorder the terms:
7 + -6x + -12x2 = -155

Solving
7 + -6x + -12x2 = -155

Solving for variable 'x'.

Reorder the terms:
7 + 155 + -6x + -12x2 = -155 + 155

Combine like terms: 7 + 155 = 162
162 + -6x + -12x2 = -155 + 155

Combine like terms: -155 + 155 = 0
162 + -6x + -12x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(27 + -1x + -2x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(27 + -1x + -2x2)' equal to zero and attempt to solve:

Simplifying
27 + -1x + -2x2 = 0

Solving
27 + -1x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-13.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '13.5' to each side of the equation.
-13.5 + 0.5x + 13.5 + x2 = 0 + 13.5

Reorder the terms:
-13.5 + 13.5 + 0.5x + x2 = 0 + 13.5

Combine like terms: -13.5 + 13.5 = 0.0
0.0 + 0.5x + x2 = 0 + 13.5
0.5x + x2 = 0 + 13.5

Combine like terms: 0 + 13.5 = 13.5
0.5x + x2 = 13.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 13.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 13.5 + 0.0625

Combine like terms: 13.5 + 0.0625 = 13.5625
0.0625 + 0.5x + x2 = 13.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 13.5625

Calculate the square root of the right side: 3.682729966

Break this problem into two subproblems by setting 
(x + 0.25) equal to 3.682729966 and -3.682729966.


Subproblem 1
x + 0.25 = 3.682729966

Simplifying
x + 0.25 = 3.682729966

Reorder the terms:
0.25 + x = 3.682729966

Solving
0.25 + x = 3.682729966

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 3.682729966 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 3.682729966 + -0.25
x = 3.682729966 + -0.25

Combine like terms: 3.682729966 + -0.25 = 3.432729966
x = 3.432729966

Simplifying
x = 3.432729966


Subproblem 2
x + 0.25 = -3.682729966

Simplifying
x + 0.25 = -3.682729966

Reorder the terms:
0.25 + x = -3.682729966

Solving
0.25 + x = -3.682729966

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -3.682729966 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -3.682729966 + -0.25
x = -3.682729966 + -0.25

Combine like terms: -3.682729966 + -0.25 = -3.932729966
x = -3.932729966

Simplifying
x = -3.932729966


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.432729966, -3.932729966}
Solution
x = {3.432729966, -3.932729966}

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