4x^2-68x+330=0

Solution for 4x^2-68x+330=0 equation:

Simplifying
4x2 + -68x + 330 = 0

Reorder the terms:
330 + -68x + 4x2 = 0

Solving
330 + -68x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(165 + -34x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(165 + -34x + 2x2)' equal to zero and attempt to solve:

Simplifying
165 + -34x + 2x2 = 0

Solving
165 + -34x + 2x2 = 0

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

Divide each side by '2'.
82.5 + -17x + x2 = 0

Move the constant term to the right:

Add '-82.5' to each side of the equation.
82.5 + -17x + -82.5 + x2 = 0 + -82.5

Reorder the terms:
82.5 + -82.5 + -17x + x2 = 0 + -82.5

Combine like terms: 82.5 + -82.5 = 0.0
0.0 + -17x + x2 = 0 + -82.5
-17x + x2 = 0 + -82.5

Combine like terms: 0 + -82.5 = -82.5
-17x + x2 = -82.5

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -82.5 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -82.5 + 72.25

Combine like terms: -82.5 + 72.25 = -10.25
72.25 + -17x + x2 = -10.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = -10.25

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.