12x^2-10x-5=0

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Solution for 12x^2-10x-5=0 equation: 


Simplifying
12x2 + -10x + -5 = 0

Reorder the terms:
-5 + -10x + 12x2 = 0

Solving
-5 + -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'.
-0.4166666667 + -0.8333333333x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + -0.8333333333x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + -0.8333333333x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + -0.8333333333x + x2 = 0 + 0.4166666667
-0.8333333333x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
-0.8333333333x + x2 = 0.4166666667

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 = 0.4166666667 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333x + x2 = 0.4166666667 + 0.1736111111

Combine like terms: 0.4166666667 + 0.1736111111 = 0.5902777778
0.1736111111 + -0.8333333333x + x2 = 0.5902777778

Factor a perfect square on the left side:
(x + -0.4166666667)(x + -0.4166666667) = 0.5902777778

Calculate the square root of the right side: 0.768295371

Break this problem into two subproblems by setting 
(x + -0.4166666667) equal to 0.768295371 and -0.768295371.


Subproblem 1
x + -0.4166666667 = 0.768295371

Simplifying
x + -0.4166666667 = 0.768295371

Reorder the terms:
-0.4166666667 + x = 0.768295371

Solving
-0.4166666667 + x = 0.768295371

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 = 0.768295371 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = 0.768295371 + 0.4166666667
x = 0.768295371 + 0.4166666667

Combine like terms: 0.768295371 + 0.4166666667 = 1.1849620377
x = 1.1849620377

Simplifying
x = 1.1849620377


Subproblem 2
x + -0.4166666667 = -0.768295371

Simplifying
x + -0.4166666667 = -0.768295371

Reorder the terms:
-0.4166666667 + x = -0.768295371

Solving
-0.4166666667 + x = -0.768295371

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 = -0.768295371 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + x = -0.768295371 + 0.4166666667
x = -0.768295371 + 0.4166666667

Combine like terms: -0.768295371 + 0.4166666667 = -0.3516287043
x = -0.3516287043

Simplifying
x = -0.3516287043


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1849620377, -0.3516287043}

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