(9x^2)-252x+330=0

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Solution for (9x^2)-252x+330=0 equation: 


Simplifying
(9x2) + -252x + 330 = 0

Reorder the terms:
330 + -252x + (9x2) = 0

Solving
330 + -252x + (9x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(110 + -84x + (3x2)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(110 + -84x + (3x2))' equal to zero and attempt to solve:

Simplifying
110 + -84x + (3x2) = 0

Solving
110 + -84x + (3x2) = 0

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

Divide each side by '3'.
36.66666667 + -28x + x2 = 0

Move the constant term to the right:

Add '-36.66666667' to each side of the equation.
36.66666667 + -28x + -36.66666667 + x2 = 0 + -36.66666667

Reorder the terms:
36.66666667 + -36.66666667 + -28x + x2 = 0 + -36.66666667

Combine like terms: 36.66666667 + -36.66666667 = 0.00000000
0.00000000 + -28x + x2 = 0 + -36.66666667
-28x + x2 = 0 + -36.66666667

Combine like terms: 0 + -36.66666667 = -36.66666667
-28x + x2 = -36.66666667

The x term is -28x.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28x + 196 + x2 = -36.66666667 + 196

Reorder the terms:
196 + -28x + x2 = -36.66666667 + 196

Combine like terms: -36.66666667 + 196 = 159.33333333
196 + -28x + x2 = 159.33333333

Factor a perfect square on the left side:
((x) + -14)((x) + -14) = 159.33333333

Calculate the square root of the right side: 12.622730819

Break this problem into two subproblems by setting 
((x) + -14) equal to 12.622730819 and -12.622730819.


Subproblem 1
(x) + -14 = 12.622730819

Simplifying
(x) + -14 = 12.622730819
x + -14 = 12.622730819

Reorder the terms:
-14 + x = 12.622730819

Solving
-14 + x = 12.622730819

Solving for variable 'x'.

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

Add '14' to each side of the equation.
-14 + 14 + x = 12.622730819 + 14

Combine like terms: -14 + 14 = 0
0 + x = 12.622730819 + 14
x = 12.622730819 + 14

Combine like terms: 12.622730819 + 14 = 26.622730819
x = 26.622730819

Simplifying
x = 26.622730819


Subproblem 2
(x) + -14 = -12.622730819

Simplifying
(x) + -14 = -12.622730819
x + -14 = -12.622730819

Reorder the terms:
-14 + x = -12.622730819

Solving
-14 + x = -12.622730819

Solving for variable 'x'.

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

Add '14' to each side of the equation.
-14 + 14 + x = -12.622730819 + 14

Combine like terms: -14 + 14 = 0
0 + x = -12.622730819 + 14
x = -12.622730819 + 14

Combine like terms: -12.622730819 + 14 = 1.377269181
x = 1.377269181

Simplifying
x = 1.377269181


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {26.622730819, 1.377269181}
Solution
x = {26.622730819, 1.377269181}

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