9x^2+12x-26=0

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Solution for 9x^2+12x-26=0 equation: 


Simplifying
9x2 + 12x + -26 = 0

Reorder the terms:
-26 + 12x + 9x2 = 0

Solving
-26 + 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'.
-2.888888889 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '2.888888889' to each side of the equation.
-2.888888889 + 1.333333333x + 2.888888889 + x2 = 0 + 2.888888889

Reorder the terms:
-2.888888889 + 2.888888889 + 1.333333333x + x2 = 0 + 2.888888889

Combine like terms: -2.888888889 + 2.888888889 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 2.888888889
1.333333333x + x2 = 0 + 2.888888889

Combine like terms: 0 + 2.888888889 = 2.888888889
1.333333333x + x2 = 2.888888889

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 = 2.888888889 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 2.888888889 + 0.4444444442

Combine like terms: 2.888888889 + 0.4444444442 = 3.3333333332
0.4444444442 + 1.333333333x + x2 = 3.3333333332

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 3.3333333332

Calculate the square root of the right side: 1.825741858

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.825741858 and -1.825741858.


Subproblem 1
x + 0.6666666665 = 1.825741858

Simplifying
x + 0.6666666665 = 1.825741858

Reorder the terms:
0.6666666665 + x = 1.825741858

Solving
0.6666666665 + x = 1.825741858

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 = 1.825741858 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 1.825741858 + -0.6666666665
x = 1.825741858 + -0.6666666665

Combine like terms: 1.825741858 + -0.6666666665 = 1.1590751915
x = 1.1590751915

Simplifying
x = 1.1590751915


Subproblem 2
x + 0.6666666665 = -1.825741858

Simplifying
x + 0.6666666665 = -1.825741858

Reorder the terms:
0.6666666665 + x = -1.825741858

Solving
0.6666666665 + x = -1.825741858

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 = -1.825741858 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -1.825741858 + -0.6666666665
x = -1.825741858 + -0.6666666665

Combine like terms: -1.825741858 + -0.6666666665 = -2.4924085245
x = -2.4924085245

Simplifying
x = -2.4924085245


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1590751915, -2.4924085245}

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