9x^2-12x-10=0

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


Simplifying
9x2 + -12x + -10 = 0

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

Solving
-10 + -12x + 9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
9 the coefficient of the squared term: 

Divide each side by '9'.
-1.111111111 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.111111111' to each side of the equation.
-1.111111111 + -1.333333333x + 1.111111111 + x2 = 0 + 1.111111111

Reorder the terms:
-1.111111111 + 1.111111111 + -1.333333333x + x2 = 0 + 1.111111111

Combine like terms: -1.111111111 + 1.111111111 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + 1.111111111
-1.333333333x + x2 = 0 + 1.111111111

Combine like terms: 0 + 1.111111111 = 1.111111111
-1.333333333x + x2 = 1.111111111

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = 1.111111111 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 1.111111111 + 0.4444444442

Combine like terms: 1.111111111 + 0.4444444442 = 1.5555555552
0.4444444442 + -1.333333333x + x2 = 1.5555555552

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 1.5555555552

Calculate the square root of the right side: 1.247219129

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.247219129 and -1.247219129.


Subproblem 1
x + -0.6666666665 = 1.247219129

Simplifying
x + -0.6666666665 = 1.247219129

Reorder the terms:
-0.6666666665 + x = 1.247219129

Solving
-0.6666666665 + x = 1.247219129

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = 1.247219129 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 1.247219129 + 0.6666666665
x = 1.247219129 + 0.6666666665

Combine like terms: 1.247219129 + 0.6666666665 = 1.9138857955
x = 1.9138857955

Simplifying
x = 1.9138857955


Subproblem 2
x + -0.6666666665 = -1.247219129

Simplifying
x + -0.6666666665 = -1.247219129

Reorder the terms:
-0.6666666665 + x = -1.247219129

Solving
-0.6666666665 + x = -1.247219129

Solving for variable 'x'.

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

Add '0.6666666665' to each side of the equation.
-0.6666666665 + 0.6666666665 + x = -1.247219129 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -1.247219129 + 0.6666666665
x = -1.247219129 + 0.6666666665

Combine like terms: -1.247219129 + 0.6666666665 = -0.5805524625
x = -0.5805524625

Simplifying
x = -0.5805524625


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.9138857955, -0.5805524625}

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