9x^2+45x-12=0

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Solution for 9x^2+45x-12=0 equation: 


Simplifying
9x2 + 45x + -12 = 0

Reorder the terms:
-12 + 45x + 9x2 = 0

Solving
-12 + 45x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 15x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + 15x + 3x2)' equal to zero and attempt to solve:

Simplifying
-4 + 15x + 3x2 = 0

Solving
-4 + 15x + 3x2 = 0

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

Divide each side by '3'.
-1.333333333 + 5x + x2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 5x + 1.333333333 + x2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 5x + x2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 5x + x2 = 0 + 1.333333333
5x + x2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
5x + x2 = 1.333333333

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 1.333333333 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1.333333333 + 6.25

Combine like terms: 1.333333333 + 6.25 = 7.583333333
6.25 + 5x + x2 = 7.583333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 7.583333333

Calculate the square root of the right side: 2.753785274

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.753785274 and -2.753785274.


Subproblem 1
x + 2.5 = 2.753785274

Simplifying
x + 2.5 = 2.753785274

Reorder the terms:
2.5 + x = 2.753785274

Solving
2.5 + x = 2.753785274

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 2.753785274 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 2.753785274 + -2.5
x = 2.753785274 + -2.5

Combine like terms: 2.753785274 + -2.5 = 0.253785274
x = 0.253785274

Simplifying
x = 0.253785274


Subproblem 2
x + 2.5 = -2.753785274

Simplifying
x + 2.5 = -2.753785274

Reorder the terms:
2.5 + x = -2.753785274

Solving
2.5 + x = -2.753785274

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -2.753785274 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -2.753785274 + -2.5
x = -2.753785274 + -2.5

Combine like terms: -2.753785274 + -2.5 = -5.253785274
x = -5.253785274

Simplifying
x = -5.253785274


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.253785274, -5.253785274}
Solution
x = {0.253785274, -5.253785274}

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