6x^2+93x+45=9

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Solution for 6x^2+93x+45=9 equation: 


Simplifying
6x2 + 93x + 45 = 9

Reorder the terms:
45 + 93x + 6x2 = 9

Solving
45 + 93x + 6x2 = 9

Solving for variable 'x'.

Reorder the terms:
45 + -9 + 93x + 6x2 = 9 + -9

Combine like terms: 45 + -9 = 36
36 + 93x + 6x2 = 9 + -9

Combine like terms: 9 + -9 = 0
36 + 93x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 31x + 2x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(12 + 31x + 2x2)' equal to zero and attempt to solve:

Simplifying
12 + 31x + 2x2 = 0

Solving
12 + 31x + 2x2 = 0

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

Divide each side by '2'.
6 + 15.5x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 15.5x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 15.5x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 15.5x + x2 = 0 + -6
15.5x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
15.5x + x2 = -6

The x term is 15.5x.  Take half its coefficient (7.75).
Square it (60.0625) and add it to both sides.

Add '60.0625' to each side of the equation.
15.5x + 60.0625 + x2 = -6 + 60.0625

Reorder the terms:
60.0625 + 15.5x + x2 = -6 + 60.0625

Combine like terms: -6 + 60.0625 = 54.0625
60.0625 + 15.5x + x2 = 54.0625

Factor a perfect square on the left side:
(x + 7.75)(x + 7.75) = 54.0625

Calculate the square root of the right side: 7.352720585

Break this problem into two subproblems by setting 
(x + 7.75) equal to 7.352720585 and -7.352720585.


Subproblem 1
x + 7.75 = 7.352720585

Simplifying
x + 7.75 = 7.352720585

Reorder the terms:
7.75 + x = 7.352720585

Solving
7.75 + x = 7.352720585

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = 7.352720585 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = 7.352720585 + -7.75
x = 7.352720585 + -7.75

Combine like terms: 7.352720585 + -7.75 = -0.397279415
x = -0.397279415

Simplifying
x = -0.397279415


Subproblem 2
x + 7.75 = -7.352720585

Simplifying
x + 7.75 = -7.352720585

Reorder the terms:
7.75 + x = -7.352720585

Solving
7.75 + x = -7.352720585

Solving for variable 'x'.

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

Add '-7.75' to each side of the equation.
7.75 + -7.75 + x = -7.352720585 + -7.75

Combine like terms: 7.75 + -7.75 = 0.00
0.00 + x = -7.352720585 + -7.75
x = -7.352720585 + -7.75

Combine like terms: -7.352720585 + -7.75 = -15.102720585
x = -15.102720585

Simplifying
x = -15.102720585


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.397279415, -15.102720585}
Solution
x = {-0.397279415, -15.102720585}

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