18x^2-108x+68=0

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Solution for 18x^2-108x+68=0 equation: 


Simplifying
18x2 + -108x + 68 = 0

Reorder the terms:
68 + -108x + 18x2 = 0

Solving
68 + -108x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(34 + -54x + 9x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(34 + -54x + 9x2)' equal to zero and attempt to solve:

Simplifying
34 + -54x + 9x2 = 0

Solving
34 + -54x + 9x2 = 0

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

Divide each side by '9'.
3.777777778 + -6x + x2 = 0

Move the constant term to the right:

Add '-3.777777778' to each side of the equation.
3.777777778 + -6x + -3.777777778 + x2 = 0 + -3.777777778

Reorder the terms:
3.777777778 + -3.777777778 + -6x + x2 = 0 + -3.777777778

Combine like terms: 3.777777778 + -3.777777778 = 0.000000000
0.000000000 + -6x + x2 = 0 + -3.777777778
-6x + x2 = 0 + -3.777777778

Combine like terms: 0 + -3.777777778 = -3.777777778
-6x + x2 = -3.777777778

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -3.777777778 + 9

Reorder the terms:
9 + -6x + x2 = -3.777777778 + 9

Combine like terms: -3.777777778 + 9 = 5.222222222
9 + -6x + x2 = 5.222222222

Factor a perfect square on the left side:
(x + -3)(x + -3) = 5.222222222

Calculate the square root of the right side: 2.2852182

Break this problem into two subproblems by setting 
(x + -3) equal to 2.2852182 and -2.2852182.


Subproblem 1
x + -3 = 2.2852182

Simplifying
x + -3 = 2.2852182

Reorder the terms:
-3 + x = 2.2852182

Solving
-3 + x = 2.2852182

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 2.2852182 + 3

Combine like terms: -3 + 3 = 0
0 + x = 2.2852182 + 3
x = 2.2852182 + 3

Combine like terms: 2.2852182 + 3 = 5.2852182
x = 5.2852182

Simplifying
x = 5.2852182


Subproblem 2
x + -3 = -2.2852182

Simplifying
x + -3 = -2.2852182

Reorder the terms:
-3 + x = -2.2852182

Solving
-3 + x = -2.2852182

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -2.2852182 + 3

Combine like terms: -3 + 3 = 0
0 + x = -2.2852182 + 3
x = -2.2852182 + 3

Combine like terms: -2.2852182 + 3 = 0.7147818
x = 0.7147818

Simplifying
x = 0.7147818


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.2852182, 0.7147818}
Solution
x = {5.2852182, 0.7147818}

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