9x^2-96x+162=0

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Solution for 9x^2-96x+162=0 equation: 


Simplifying
9x2 + -96x + 162 = 0

Reorder the terms:
162 + -96x + 9x2 = 0

Solving
162 + -96x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(54 + -32x + 3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(54 + -32x + 3x2)' equal to zero and attempt to solve:

Simplifying
54 + -32x + 3x2 = 0

Solving
54 + -32x + 3x2 = 0

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

Divide each side by '3'.
18 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -10.66666667x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -10.66666667x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -10.66666667x + x2 = 0 + -18
-10.66666667x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-10.66666667x + x2 = -18

The x term is -10.66666667x.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x + 28.44444446 + x2 = -18 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = -18 + 28.44444446

Combine like terms: -18 + 28.44444446 = 10.44444446
28.44444446 + -10.66666667x + x2 = 10.44444446

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 10.44444446

Calculate the square root of the right side: 3.231786574

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 3.231786574 and -3.231786574.


Subproblem 1
x + -5.333333335 = 3.231786574

Simplifying
x + -5.333333335 = 3.231786574

Reorder the terms:
-5.333333335 + x = 3.231786574

Solving
-5.333333335 + x = 3.231786574

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = 3.231786574 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = 3.231786574 + 5.333333335
x = 3.231786574 + 5.333333335

Combine like terms: 3.231786574 + 5.333333335 = 8.565119909
x = 8.565119909

Simplifying
x = 8.565119909


Subproblem 2
x + -5.333333335 = -3.231786574

Simplifying
x + -5.333333335 = -3.231786574

Reorder the terms:
-5.333333335 + x = -3.231786574

Solving
-5.333333335 + x = -3.231786574

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = -3.231786574 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = -3.231786574 + 5.333333335
x = -3.231786574 + 5.333333335

Combine like terms: -3.231786574 + 5.333333335 = 2.101546761
x = 2.101546761

Simplifying
x = 2.101546761


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.565119909, 2.101546761}
Solution
x = {8.565119909, 2.101546761}

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