9x^2+18x-66=0

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Solution for 9x^2+18x-66=0 equation: 


Simplifying
9x2 + 18x + -66 = 0

Reorder the terms:
-66 + 18x + 9x2 = 0

Solving
-66 + 18x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-22 + 6x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-22 + 6x + 3x2)' equal to zero and attempt to solve:

Simplifying
-22 + 6x + 3x2 = 0

Solving
-22 + 6x + 3x2 = 0

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

Divide each side by '3'.
-7.333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + 2x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + 2x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 7.333333333
2x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
2x + x2 = 7.333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 7.333333333 + 1

Reorder the terms:
1 + 2x + x2 = 7.333333333 + 1

Combine like terms: 7.333333333 + 1 = 8.333333333
1 + 2x + x2 = 8.333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 8.333333333

Calculate the square root of the right side: 2.886751346

Break this problem into two subproblems by setting 
(x + 1) equal to 2.886751346 and -2.886751346.


Subproblem 1
x + 1 = 2.886751346

Simplifying
x + 1 = 2.886751346

Reorder the terms:
1 + x = 2.886751346

Solving
1 + x = 2.886751346

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 2.886751346 + -1

Combine like terms: 1 + -1 = 0
0 + x = 2.886751346 + -1
x = 2.886751346 + -1

Combine like terms: 2.886751346 + -1 = 1.886751346
x = 1.886751346

Simplifying
x = 1.886751346


Subproblem 2
x + 1 = -2.886751346

Simplifying
x + 1 = -2.886751346

Reorder the terms:
1 + x = -2.886751346

Solving
1 + x = -2.886751346

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -2.886751346 + -1

Combine like terms: 1 + -1 = 0
0 + x = -2.886751346 + -1
x = -2.886751346 + -1

Combine like terms: -2.886751346 + -1 = -3.886751346
x = -3.886751346

Simplifying
x = -3.886751346


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.886751346, -3.886751346}
Solution
x = {1.886751346, -3.886751346}

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