12x^2+28x-125=0

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Solution for 12x^2+28x-125=0 equation: 


Simplifying
12x2 + 28x + -125 = 0

Reorder the terms:
-125 + 28x + 12x2 = 0

Solving
-125 + 28x + 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'.
-10.41666667 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '10.41666667' to each side of the equation.
-10.41666667 + 2.333333333x + 10.41666667 + x2 = 0 + 10.41666667

Reorder the terms:
-10.41666667 + 10.41666667 + 2.333333333x + x2 = 0 + 10.41666667

Combine like terms: -10.41666667 + 10.41666667 = 0.00000000
0.00000000 + 2.333333333x + x2 = 0 + 10.41666667
2.333333333x + x2 = 0 + 10.41666667

Combine like terms: 0 + 10.41666667 = 10.41666667
2.333333333x + x2 = 10.41666667

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 10.41666667 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 10.41666667 + 1.361111112

Combine like terms: 10.41666667 + 1.361111112 = 11.777777782
1.361111112 + 2.333333333x + x2 = 11.777777782

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 11.777777782

Calculate the square root of the right side: 3.431876714

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 3.431876714 and -3.431876714.


Subproblem 1
x + 1.166666667 = 3.431876714

Simplifying
x + 1.166666667 = 3.431876714

Reorder the terms:
1.166666667 + x = 3.431876714

Solving
1.166666667 + x = 3.431876714

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = 3.431876714 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = 3.431876714 + -1.166666667
x = 3.431876714 + -1.166666667

Combine like terms: 3.431876714 + -1.166666667 = 2.265210047
x = 2.265210047

Simplifying
x = 2.265210047


Subproblem 2
x + 1.166666667 = -3.431876714

Simplifying
x + 1.166666667 = -3.431876714

Reorder the terms:
1.166666667 + x = -3.431876714

Solving
1.166666667 + x = -3.431876714

Solving for variable 'x'.

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

Add '-1.166666667' to each side of the equation.
1.166666667 + -1.166666667 + x = -3.431876714 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + x = -3.431876714 + -1.166666667
x = -3.431876714 + -1.166666667

Combine like terms: -3.431876714 + -1.166666667 = -4.598543381
x = -4.598543381

Simplifying
x = -4.598543381


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.265210047, -4.598543381}

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