0=9x^2+6x-888

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Solution for 0=9x^2+6x-888 equation:


Simplifying
0 = 9x2 + 6x + -888

Reorder the terms:
0 = -888 + 6x + 9x2

Solving
0 = -888 + 6x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + 888 = 888
888 + -6x + -9x2 = -888 + 6x + 9x2 + 888 + -6x + -9x2

Reorder the terms:
888 + -6x + -9x2 = -888 + 888 + 6x + -6x + 9x2 + -9x2

Combine like terms: -888 + 888 = 0
888 + -6x + -9x2 = 0 + 6x + -6x + 9x2 + -9x2
888 + -6x + -9x2 = 6x + -6x + 9x2 + -9x2

Combine like terms: 6x + -6x = 0
888 + -6x + -9x2 = 0 + 9x2 + -9x2
888 + -6x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
888 + -6x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(296 + -2x + -3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(296 + -2x + -3x2)' equal to zero and attempt to solve:

Simplifying
296 + -2x + -3x2 = 0

Solving
296 + -2x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-98.66666667 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '98.66666667' to each side of the equation.
-98.66666667 + 0.6666666667x + 98.66666667 + x2 = 0 + 98.66666667

Reorder the terms:
-98.66666667 + 98.66666667 + 0.6666666667x + x2 = 0 + 98.66666667

Combine like terms: -98.66666667 + 98.66666667 = 0.00000000
0.00000000 + 0.6666666667x + x2 = 0 + 98.66666667
0.6666666667x + x2 = 0 + 98.66666667

Combine like terms: 0 + 98.66666667 = 98.66666667
0.6666666667x + x2 = 98.66666667

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 98.66666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 98.66666667 + 0.1111111112

Combine like terms: 98.66666667 + 0.1111111112 = 98.7777777812
0.1111111112 + 0.6666666667x + x2 = 98.7777777812

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 98.7777777812

Calculate the square root of the right side: 9.938701011

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 9.938701011 and -9.938701011.


Subproblem 1
x + 0.3333333334 = 9.938701011

Simplifying
x + 0.3333333334 = 9.938701011

Reorder the terms:
0.3333333334 + x = 9.938701011

Solving
0.3333333334 + x = 9.938701011

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 9.938701011 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 9.938701011 + -0.3333333334
x = 9.938701011 + -0.3333333334

Combine like terms: 9.938701011 + -0.3333333334 = 9.6053676776
x = 9.6053676776

Simplifying
x = 9.6053676776


Subproblem 2
x + 0.3333333334 = -9.938701011

Simplifying
x + 0.3333333334 = -9.938701011

Reorder the terms:
0.3333333334 + x = -9.938701011

Solving
0.3333333334 + x = -9.938701011

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -9.938701011 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -9.938701011 + -0.3333333334
x = -9.938701011 + -0.3333333334

Combine like terms: -9.938701011 + -0.3333333334 = -10.2720343444
x = -10.2720343444

Simplifying
x = -10.2720343444


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.6053676776, -10.2720343444}
Solution
x = {9.6053676776, -10.2720343444}

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