12x^2-23x-10=0

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Solution for 12x^2-23x-10=0 equation: 


Simplifying
12x2 + -23x + -10 = 0

Reorder the terms:
-10 + -23x + 12x2 = 0

Solving
-10 + -23x + 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'.
-0.8333333333 + -1.916666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -1.916666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -1.916666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -1.916666667x + x2 = 0 + 0.8333333333
-1.916666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-1.916666667x + x2 = 0.8333333333

The x term is -1.916666667x.  Take half its coefficient (-0.9583333335).
Square it (0.9184027781) and add it to both sides.

Add '0.9184027781' to each side of the equation.
-1.916666667x + 0.9184027781 + x2 = 0.8333333333 + 0.9184027781

Reorder the terms:
0.9184027781 + -1.916666667x + x2 = 0.8333333333 + 0.9184027781

Combine like terms: 0.8333333333 + 0.9184027781 = 1.7517361114
0.9184027781 + -1.916666667x + x2 = 1.7517361114

Factor a perfect square on the left side:
(x + -0.9583333335)(x + -0.9583333335) = 1.7517361114

Calculate the square root of the right side: 1.323531681

Break this problem into two subproblems by setting 
(x + -0.9583333335) equal to 1.323531681 and -1.323531681.


Subproblem 1
x + -0.9583333335 = 1.323531681

Simplifying
x + -0.9583333335 = 1.323531681

Reorder the terms:
-0.9583333335 + x = 1.323531681

Solving
-0.9583333335 + x = 1.323531681

Solving for variable 'x'.

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

Add '0.9583333335' to each side of the equation.
-0.9583333335 + 0.9583333335 + x = 1.323531681 + 0.9583333335

Combine like terms: -0.9583333335 + 0.9583333335 = 0.0000000000
0.0000000000 + x = 1.323531681 + 0.9583333335
x = 1.323531681 + 0.9583333335

Combine like terms: 1.323531681 + 0.9583333335 = 2.2818650145
x = 2.2818650145

Simplifying
x = 2.2818650145


Subproblem 2
x + -0.9583333335 = -1.323531681

Simplifying
x + -0.9583333335 = -1.323531681

Reorder the terms:
-0.9583333335 + x = -1.323531681

Solving
-0.9583333335 + x = -1.323531681

Solving for variable 'x'.

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

Add '0.9583333335' to each side of the equation.
-0.9583333335 + 0.9583333335 + x = -1.323531681 + 0.9583333335

Combine like terms: -0.9583333335 + 0.9583333335 = 0.0000000000
0.0000000000 + x = -1.323531681 + 0.9583333335
x = -1.323531681 + 0.9583333335

Combine like terms: -1.323531681 + 0.9583333335 = -0.3651983475
x = -0.3651983475

Simplifying
x = -0.3651983475


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.2818650145, -0.3651983475}

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