9x^2+42x-180=0

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Solution for 9x^2+42x-180=0 equation: 


Simplifying
9x2 + 42x + -180 = 0

Reorder the terms:
-180 + 42x + 9x2 = 0

Solving
-180 + 42x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 14x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + 14x + 3x2)' equal to zero and attempt to solve:

Simplifying
-60 + 14x + 3x2 = 0

Solving
-60 + 14x + 3x2 = 0

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

Divide each side by '3'.
-20 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 4.666666667x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + 4.666666667x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 4.666666667x + x2 = 0 + 20
4.666666667x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
4.666666667x + x2 = 20

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 20 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 20 + 5.444444448

Combine like terms: 20 + 5.444444448 = 25.444444448
5.444444448 + 4.666666667x + x2 = 25.444444448

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 25.444444448

Calculate the square root of the right side: 5.04424865

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 5.04424865 and -5.04424865.


Subproblem 1
x + 2.333333334 = 5.04424865

Simplifying
x + 2.333333334 = 5.04424865

Reorder the terms:
2.333333334 + x = 5.04424865

Solving
2.333333334 + x = 5.04424865

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 5.04424865 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 5.04424865 + -2.333333334
x = 5.04424865 + -2.333333334

Combine like terms: 5.04424865 + -2.333333334 = 2.710915316
x = 2.710915316

Simplifying
x = 2.710915316


Subproblem 2
x + 2.333333334 = -5.04424865

Simplifying
x + 2.333333334 = -5.04424865

Reorder the terms:
2.333333334 + x = -5.04424865

Solving
2.333333334 + x = -5.04424865

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -5.04424865 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -5.04424865 + -2.333333334
x = -5.04424865 + -2.333333334

Combine like terms: -5.04424865 + -2.333333334 = -7.377581984
x = -7.377581984

Simplifying
x = -7.377581984


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.710915316, -7.377581984}
Solution
x = {2.710915316, -7.377581984}

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