-45x^2+66x-30=0

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Solution for -45x^2+66x-30=0 equation: 


Simplifying
-45x2 + 66x + -30 = 0

Reorder the terms:
-30 + 66x + -45x2 = 0

Solving
-30 + 66x + -45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 22x + -15x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-10 + 22x + -15x2)' equal to zero and attempt to solve:

Simplifying
-10 + 22x + -15x2 = 0

Solving
-10 + 22x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
0.6666666667 + -1.466666667x + x2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + -1.466666667x + -0.6666666667 + x2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + -1.466666667x + x2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + -1.466666667x + x2 = 0 + -0.6666666667
-1.466666667x + x2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
-1.466666667x + x2 = -0.6666666667

The x term is -1.466666667x.  Take half its coefficient (-0.7333333335).
Square it (0.5377777780) and add it to both sides.

Add '0.5377777780' to each side of the equation.
-1.466666667x + 0.5377777780 + x2 = -0.6666666667 + 0.5377777780

Reorder the terms:
0.5377777780 + -1.466666667x + x2 = -0.6666666667 + 0.5377777780

Combine like terms: -0.6666666667 + 0.5377777780 = -0.1288888887
0.5377777780 + -1.466666667x + x2 = -0.1288888887

Factor a perfect square on the left side:
(x + -0.7333333335)(x + -0.7333333335) = -0.1288888887

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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