36x^2-120x+240=

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Solution for 36x^2-120x+240= equation: 


Simplifying
36x2 + -120x + 240 = 0

Reorder the terms:
240 + -120x + 36x2 = 0

Solving
240 + -120x + 36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12'.
12(20 + -10x + 3x2) = 0

Ignore the factor 12.

Subproblem 1
Set the factor '(20 + -10x + 3x2)' equal to zero and attempt to solve:

Simplifying
20 + -10x + 3x2 = 0

Solving
20 + -10x + 3x2 = 0

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

Divide each side by '3'.
6.666666667 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -3.333333333x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -3.333333333x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + -6.666666667
-3.333333333x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-3.333333333x + x2 = -6.666666667

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -6.666666667 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -6.666666667 + 2.777777779

Combine like terms: -6.666666667 + 2.777777779 = -3.888888888
2.777777779 + -3.333333333x + x2 = -3.888888888

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = -3.888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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