9x^2+72x+3=0

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Solution for 9x^2+72x+3=0 equation: 


Simplifying
9x2 + 72x + 3 = 0

Reorder the terms:
3 + 72x + 9x2 = 0

Solving
3 + 72x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 24x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + 24x + 3x2)' equal to zero and attempt to solve:

Simplifying
1 + 24x + 3x2 = 0

Solving
1 + 24x + 3x2 = 0

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

Divide each side by '3'.
0.3333333333 + 8x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 8x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 8x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 8x + x2 = 0 + -0.3333333333
8x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
8x + x2 = -0.3333333333

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -0.3333333333 + 16

Reorder the terms:
16 + 8x + x2 = -0.3333333333 + 16

Combine like terms: -0.3333333333 + 16 = 15.6666666667
16 + 8x + x2 = 15.6666666667

Factor a perfect square on the left side:
(x + 4)(x + 4) = 15.6666666667

Calculate the square root of the right side: 3.958114029

Break this problem into two subproblems by setting 
(x + 4) equal to 3.958114029 and -3.958114029.


Subproblem 1
x + 4 = 3.958114029

Simplifying
x + 4 = 3.958114029

Reorder the terms:
4 + x = 3.958114029

Solving
4 + x = 3.958114029

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 3.958114029 + -4

Combine like terms: 4 + -4 = 0
0 + x = 3.958114029 + -4
x = 3.958114029 + -4

Combine like terms: 3.958114029 + -4 = -0.041885971
x = -0.041885971

Simplifying
x = -0.041885971


Subproblem 2
x + 4 = -3.958114029

Simplifying
x + 4 = -3.958114029

Reorder the terms:
4 + x = -3.958114029

Solving
4 + x = -3.958114029

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -3.958114029 + -4

Combine like terms: 4 + -4 = 0
0 + x = -3.958114029 + -4
x = -3.958114029 + -4

Combine like terms: -3.958114029 + -4 = -7.958114029
x = -7.958114029

Simplifying
x = -7.958114029


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.041885971, -7.958114029}
Solution
x = {-0.041885971, -7.958114029}

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