9x^2-66x+90=0

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Solution for 9x^2-66x+90=0 equation: 


Simplifying
9x2 + -66x + 90 = 0

Reorder the terms:
90 + -66x + 9x2 = 0

Solving
90 + -66x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + -22x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(30 + -22x + 3x2)' equal to zero and attempt to solve:

Simplifying
30 + -22x + 3x2 = 0

Solving
30 + -22x + 3x2 = 0

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

Divide each side by '3'.
10 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -7.333333333x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -7.333333333x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -7.333333333x + x2 = 0 + -10
-7.333333333x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-7.333333333x + x2 = -10

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = -10 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = -10 + 13.44444445

Combine like terms: -10 + 13.44444445 = 3.44444445
13.44444445 + -7.333333333x + x2 = 3.44444445

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 3.44444445

Calculate the square root of the right side: 1.855921456

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 1.855921456 and -1.855921456.


Subproblem 1
x + -3.666666667 = 1.855921456

Simplifying
x + -3.666666667 = 1.855921456

Reorder the terms:
-3.666666667 + x = 1.855921456

Solving
-3.666666667 + x = 1.855921456

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 1.855921456 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 1.855921456 + 3.666666667
x = 1.855921456 + 3.666666667

Combine like terms: 1.855921456 + 3.666666667 = 5.522588123
x = 5.522588123

Simplifying
x = 5.522588123


Subproblem 2
x + -3.666666667 = -1.855921456

Simplifying
x + -3.666666667 = -1.855921456

Reorder the terms:
-3.666666667 + x = -1.855921456

Solving
-3.666666667 + x = -1.855921456

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -1.855921456 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -1.855921456 + 3.666666667
x = -1.855921456 + 3.666666667

Combine like terms: -1.855921456 + 3.666666667 = 1.810745211
x = 1.810745211

Simplifying
x = 1.810745211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.522588123, 1.810745211}
Solution
x = {5.522588123, 1.810745211}

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