12x^2+10x-9=0

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Solution for 12x^2+10x-9=0 equation: 


Simplifying
12x2 + 10x + -9 = 0

Reorder the terms:
-9 + 10x + 12x2 = 0

Solving
-9 + 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'.
-0.75 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 0.8333333333x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 0.8333333333x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 0.8333333333x + x2 = 0 + 0.75
0.8333333333x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
0.8333333333x + x2 = 0.75

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 = 0.75 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = 0.75 + 0.1736111111

Combine like terms: 0.75 + 0.1736111111 = 0.9236111111
0.1736111111 + 0.8333333333x + x2 = 0.9236111111

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = 0.9236111111

Calculate the square root of the right side: 0.961046883

Break this problem into two subproblems by setting 
(x + 0.4166666667) equal to 0.961046883 and -0.961046883.


Subproblem 1
x + 0.4166666667 = 0.961046883

Simplifying
x + 0.4166666667 = 0.961046883

Reorder the terms:
0.4166666667 + x = 0.961046883

Solving
0.4166666667 + x = 0.961046883

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 = 0.961046883 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = 0.961046883 + -0.4166666667
x = 0.961046883 + -0.4166666667

Combine like terms: 0.961046883 + -0.4166666667 = 0.5443802163
x = 0.5443802163

Simplifying
x = 0.5443802163


Subproblem 2
x + 0.4166666667 = -0.961046883

Simplifying
x + 0.4166666667 = -0.961046883

Reorder the terms:
0.4166666667 + x = -0.961046883

Solving
0.4166666667 + x = -0.961046883

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 = -0.961046883 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + x = -0.961046883 + -0.4166666667
x = -0.961046883 + -0.4166666667

Combine like terms: -0.961046883 + -0.4166666667 = -1.3777135497
x = -1.3777135497

Simplifying
x = -1.3777135497


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5443802163, -1.3777135497}

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