12x^2+40x-25=0

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Solution for 12x^2+40x-25=0 equation: 


Simplifying
12x2 + 40x + -25 = 0

Reorder the terms:
-25 + 40x + 12x2 = 0

Solving
-25 + 40x + 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 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '2.083333333' to each side of the equation.
-2.083333333 + 3.333333333x + 2.083333333 + x2 = 0 + 2.083333333

Reorder the terms:
-2.083333333 + 2.083333333 + 3.333333333x + x2 = 0 + 2.083333333

Combine like terms: -2.083333333 + 2.083333333 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + 2.083333333
3.333333333x + x2 = 0 + 2.083333333

Combine like terms: 0 + 2.083333333 = 2.083333333
3.333333333x + x2 = 2.083333333

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = 2.083333333 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 2.083333333 + 2.777777779

Combine like terms: 2.083333333 + 2.777777779 = 4.861111112
2.777777779 + 3.333333333x + x2 = 4.861111112

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 4.861111112

Calculate the square root of the right side: 2.204792759

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 2.204792759 and -2.204792759.


Subproblem 1
x + 1.666666667 = 2.204792759

Simplifying
x + 1.666666667 = 2.204792759

Reorder the terms:
1.666666667 + x = 2.204792759

Solving
1.666666667 + x = 2.204792759

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = 2.204792759 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 2.204792759 + -1.666666667
x = 2.204792759 + -1.666666667

Combine like terms: 2.204792759 + -1.666666667 = 0.538126092
x = 0.538126092

Simplifying
x = 0.538126092


Subproblem 2
x + 1.666666667 = -2.204792759

Simplifying
x + 1.666666667 = -2.204792759

Reorder the terms:
1.666666667 + x = -2.204792759

Solving
1.666666667 + x = -2.204792759

Solving for variable 'x'.

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

Add '-1.666666667' to each side of the equation.
1.666666667 + -1.666666667 + x = -2.204792759 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -2.204792759 + -1.666666667
x = -2.204792759 + -1.666666667

Combine like terms: -2.204792759 + -1.666666667 = -3.871459426
x = -3.871459426

Simplifying
x = -3.871459426


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.538126092, -3.871459426}

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