12x^2+76x-25=0

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Solution for 12x^2+76x-25=0 equation: 


Simplifying
12x2 + 76x + -25 = 0

Reorder the terms:
-25 + 76x + 12x2 = 0

Solving
-25 + 76x + 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'.
-2.083333333 + 6.333333333x + x2 = 0

Move the constant term to the right:

Add '2.083333333' to each side of the equation.
-2.083333333 + 6.333333333x + 2.083333333 + x2 = 0 + 2.083333333

Reorder the terms:
-2.083333333 + 2.083333333 + 6.333333333x + x2 = 0 + 2.083333333

Combine like terms: -2.083333333 + 2.083333333 = 0.000000000
0.000000000 + 6.333333333x + x2 = 0 + 2.083333333
6.333333333x + x2 = 0 + 2.083333333

Combine like terms: 0 + 2.083333333 = 2.083333333
6.333333333x + x2 = 2.083333333

The x term is 6.333333333x.  Take half its coefficient (3.166666667).
Square it (10.02777778) and add it to both sides.

Add '10.02777778' to each side of the equation.
6.333333333x + 10.02777778 + x2 = 2.083333333 + 10.02777778

Reorder the terms:
10.02777778 + 6.333333333x + x2 = 2.083333333 + 10.02777778

Combine like terms: 2.083333333 + 10.02777778 = 12.111111113
10.02777778 + 6.333333333x + x2 = 12.111111113

Factor a perfect square on the left side:
(x + 3.166666667)(x + 3.166666667) = 12.111111113

Calculate the square root of the right side: 3.48010217

Break this problem into two subproblems by setting 
(x + 3.166666667) equal to 3.48010217 and -3.48010217.


Subproblem 1
x + 3.166666667 = 3.48010217

Simplifying
x + 3.166666667 = 3.48010217

Reorder the terms:
3.166666667 + x = 3.48010217

Solving
3.166666667 + x = 3.48010217

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = 3.48010217 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = 3.48010217 + -3.166666667
x = 3.48010217 + -3.166666667

Combine like terms: 3.48010217 + -3.166666667 = 0.313435503
x = 0.313435503

Simplifying
x = 0.313435503


Subproblem 2
x + 3.166666667 = -3.48010217

Simplifying
x + 3.166666667 = -3.48010217

Reorder the terms:
3.166666667 + x = -3.48010217

Solving
3.166666667 + x = -3.48010217

Solving for variable 'x'.

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

Add '-3.166666667' to each side of the equation.
3.166666667 + -3.166666667 + x = -3.48010217 + -3.166666667

Combine like terms: 3.166666667 + -3.166666667 = 0.000000000
0.000000000 + x = -3.48010217 + -3.166666667
x = -3.48010217 + -3.166666667

Combine like terms: -3.48010217 + -3.166666667 = -6.646768837
x = -6.646768837

Simplifying
x = -6.646768837


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.313435503, -6.646768837}

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