69+318x+9x^2=0

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Solution for 69+318x+9x^2=0 equation: 


Simplifying
69 + 318x + 9x2 = 0

Solving
69 + 318x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(23 + 106x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(23 + 106x + 3x2)' equal to zero and attempt to solve:

Simplifying
23 + 106x + 3x2 = 0

Solving
23 + 106x + 3x2 = 0

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

Divide each side by '3'.
7.666666667 + 35.33333333x + x2 = 0

Move the constant term to the right:

Add '-7.666666667' to each side of the equation.
7.666666667 + 35.33333333x + -7.666666667 + x2 = 0 + -7.666666667

Reorder the terms:
7.666666667 + -7.666666667 + 35.33333333x + x2 = 0 + -7.666666667

Combine like terms: 7.666666667 + -7.666666667 = 0.000000000
0.000000000 + 35.33333333x + x2 = 0 + -7.666666667
35.33333333x + x2 = 0 + -7.666666667

Combine like terms: 0 + -7.666666667 = -7.666666667
35.33333333x + x2 = -7.666666667

The x term is 35.33333333x.  Take half its coefficient (17.66666667).
Square it (312.1111112) and add it to both sides.

Add '312.1111112' to each side of the equation.
35.33333333x + 312.1111112 + x2 = -7.666666667 + 312.1111112

Reorder the terms:
312.1111112 + 35.33333333x + x2 = -7.666666667 + 312.1111112

Combine like terms: -7.666666667 + 312.1111112 = 304.444444533
312.1111112 + 35.33333333x + x2 = 304.444444533

Factor a perfect square on the left side:
(x + 17.66666667)(x + 17.66666667) = 304.444444533

Calculate the square root of the right side: 17.44833644

Break this problem into two subproblems by setting 
(x + 17.66666667) equal to 17.44833644 and -17.44833644.


Subproblem 1
x + 17.66666667 = 17.44833644

Simplifying
x + 17.66666667 = 17.44833644

Reorder the terms:
17.66666667 + x = 17.44833644

Solving
17.66666667 + x = 17.44833644

Solving for variable 'x'.

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

Add '-17.66666667' to each side of the equation.
17.66666667 + -17.66666667 + x = 17.44833644 + -17.66666667

Combine like terms: 17.66666667 + -17.66666667 = 0.00000000
0.00000000 + x = 17.44833644 + -17.66666667
x = 17.44833644 + -17.66666667

Combine like terms: 17.44833644 + -17.66666667 = -0.21833023
x = -0.21833023

Simplifying
x = -0.21833023


Subproblem 2
x + 17.66666667 = -17.44833644

Simplifying
x + 17.66666667 = -17.44833644

Reorder the terms:
17.66666667 + x = -17.44833644

Solving
17.66666667 + x = -17.44833644

Solving for variable 'x'.

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

Add '-17.66666667' to each side of the equation.
17.66666667 + -17.66666667 + x = -17.44833644 + -17.66666667

Combine like terms: 17.66666667 + -17.66666667 = 0.00000000
0.00000000 + x = -17.44833644 + -17.66666667
x = -17.44833644 + -17.66666667

Combine like terms: -17.44833644 + -17.66666667 = -35.11500311
x = -35.11500311

Simplifying
x = -35.11500311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.21833023, -35.11500311}
Solution
x = {-0.21833023, -35.11500311}

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