-9x^2+12x+7=0

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Solution for -9x^2+12x+7=0 equation: 


Simplifying
-9x2 + 12x + 7 = 0

Reorder the terms:
7 + 12x + -9x2 = 0

Solving
7 + 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'.
-0.7777777778 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '0.7777777778' to each side of the equation.
-0.7777777778 + -1.333333333x + 0.7777777778 + x2 = 0 + 0.7777777778

Reorder the terms:
-0.7777777778 + 0.7777777778 + -1.333333333x + x2 = 0 + 0.7777777778

Combine like terms: -0.7777777778 + 0.7777777778 = 0.0000000000
0.0000000000 + -1.333333333x + x2 = 0 + 0.7777777778
-1.333333333x + x2 = 0 + 0.7777777778

Combine like terms: 0 + 0.7777777778 = 0.7777777778
-1.333333333x + x2 = 0.7777777778

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 = 0.7777777778 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = 0.7777777778 + 0.4444444442

Combine like terms: 0.7777777778 + 0.4444444442 = 1.222222222
0.4444444442 + -1.333333333x + x2 = 1.222222222

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = 1.222222222

Calculate the square root of the right side: 1.105541597

Break this problem into two subproblems by setting 
(x + -0.6666666665) equal to 1.105541597 and -1.105541597.


Subproblem 1
x + -0.6666666665 = 1.105541597

Simplifying
x + -0.6666666665 = 1.105541597

Reorder the terms:
-0.6666666665 + x = 1.105541597

Solving
-0.6666666665 + x = 1.105541597

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 = 1.105541597 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = 1.105541597 + 0.6666666665
x = 1.105541597 + 0.6666666665

Combine like terms: 1.105541597 + 0.6666666665 = 1.7722082635
x = 1.7722082635

Simplifying
x = 1.7722082635


Subproblem 2
x + -0.6666666665 = -1.105541597

Simplifying
x + -0.6666666665 = -1.105541597

Reorder the terms:
-0.6666666665 + x = -1.105541597

Solving
-0.6666666665 + x = -1.105541597

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 = -1.105541597 + 0.6666666665

Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000
0.0000000000 + x = -1.105541597 + 0.6666666665
x = -1.105541597 + 0.6666666665

Combine like terms: -1.105541597 + 0.6666666665 = -0.4388749305
x = -0.4388749305

Simplifying
x = -0.4388749305


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.7722082635, -0.4388749305}

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