12x^2-10x-15=0

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Solution for 12x^2-10x-15=0 equation: 


Simplifying
12x2 + -10x + -15 = 0

Reorder the terms:
-15 + -10x + 12x2 = 0

Solving
-15 + -10x + 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'.
-1.25 + -0.8333333333x + x2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + -0.8333333333x + 1.25 + x2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + -0.8333333333x + x2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + -0.8333333333x + x2 = 0 + 1.25
-0.8333333333x + x2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
-0.8333333333x + x2 = 1.25

The x term is -0.8333333333x.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333x + 0.1736111111 + x2 = 1.25 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = 1.25 + 0.1736111111

Combine like terms: 1.25 + 0.1736111111 = 1.4236111111
0.1736111111 + -0.8333333333x + x2 = 1.4236111111

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 1.4236111111

Calculate the square root of the right side: 1.193151755

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 1.193151755 and -1.193151755.


Subproblem 1
x + -0.4166666667 = 1.193151755

Simplifying
x + -0.4166666667 = 1.193151755

Reorder the terms:
-0.4166666667 + x = 1.193151755

Solving
-0.4166666667 + x = 1.193151755

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = 1.193151755 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 1.193151755 + 0.4166666667
x = 1.193151755 + 0.4166666667

Combine like terms: 1.193151755 + 0.4166666667 = 1.6098184217
x = 1.6098184217

Simplifying
x = 1.6098184217


Subproblem 2
x + -0.4166666667 = -1.193151755

Simplifying
x + -0.4166666667 = -1.193151755

Reorder the terms:
-0.4166666667 + x = -1.193151755

Solving
-0.4166666667 + x = -1.193151755

Solving for variable 'x'.

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

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.4166666667 + x = -1.193151755 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -1.193151755 + 0.4166666667
x = -1.193151755 + 0.4166666667

Combine like terms: -1.193151755 + 0.4166666667 = -0.7764850883
x = -0.7764850883

Simplifying
x = -0.7764850883


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.6098184217, -0.7764850883}

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