9x^2=12x+2

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Solution for 9x^2=12x+2 equation: 


Simplifying
9x2 = 12x + 2

Reorder the terms:
9x2 = 2 + 12x

Solving
9x2 = 2 + 12x

Solving for variable 'x'.

Reorder the terms:
-2 + -12x + 9x2 = 2 + 12x + -2 + -12x

Reorder the terms:
-2 + -12x + 9x2 = 2 + -2 + 12x + -12x

Combine like terms: 2 + -2 = 0
-2 + -12x + 9x2 = 0 + 12x + -12x
-2 + -12x + 9x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-2 + -12x + 9x2 = 0

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

Divide each side by '9'.
-0.2222222222 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.2222222222' to each side of the equation.
-0.2222222222 + -1.333333333x + 0.2222222222 + x2 = 0 + 0.2222222222

Reorder the terms:
-0.2222222222 + 0.2222222222 + -1.333333333x + x2 = 0 + 0.2222222222

Combine like terms: -0.2222222222 + 0.2222222222 = 0.0000000000
0.0000000000 + -1.333333333x + x2 = 0 + 0.2222222222
-1.333333333x + x2 = 0 + 0.2222222222

Combine like terms: 0 + 0.2222222222 = 0.2222222222
-1.333333333x + x2 = 0.2222222222

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 = 0.2222222222 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 0.2222222222 + 0.4444444442

Combine like terms: 0.2222222222 + 0.4444444442 = 0.6666666664
0.4444444442 + -1.333333333x + x2 = 0.6666666664

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 0.6666666664

Calculate the square root of the right side: 0.816496581

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 0.816496581 and -0.816496581.


Subproblem 1
x + -0.6666666665 = 0.816496581

Simplifying
x + -0.6666666665 = 0.816496581

Reorder the terms:
-0.6666666665 + x = 0.816496581

Solving
-0.6666666665 + x = 0.816496581

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 = 0.816496581 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 0.816496581 + 0.6666666665
x = 0.816496581 + 0.6666666665

Combine like terms: 0.816496581 + 0.6666666665 = 1.4831632475
x = 1.4831632475

Simplifying
x = 1.4831632475


Subproblem 2
x + -0.6666666665 = -0.816496581

Simplifying
x + -0.6666666665 = -0.816496581

Reorder the terms:
-0.6666666665 + x = -0.816496581

Solving
-0.6666666665 + x = -0.816496581

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 = -0.816496581 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -0.816496581 + 0.6666666665
x = -0.816496581 + 0.6666666665

Combine like terms: -0.816496581 + 0.6666666665 = -0.1498299145
x = -0.1498299145

Simplifying
x = -0.1498299145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.4831632475, -0.1498299145}

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