-4y^2+28y-58=0

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Solution for -4y^2+28y-58=0 equation: 


Simplifying
-4y2 + 28y + -58 = 0

Reorder the terms:
-58 + 28y + -4y2 = 0

Solving
-58 + 28y + -4y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-29 + 14y + -2y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-29 + 14y + -2y2)' equal to zero and attempt to solve:

Simplifying
-29 + 14y + -2y2 = 0

Solving
-29 + 14y + -2y2 = 0

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

Divide each side by '-2'.
14.5 + -7y + y2 = 0

Move the constant term to the right:

Add '-14.5' to each side of the equation.
14.5 + -7y + -14.5 + y2 = 0 + -14.5

Reorder the terms:
14.5 + -14.5 + -7y + y2 = 0 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + -7y + y2 = 0 + -14.5
-7y + y2 = 0 + -14.5

Combine like terms: 0 + -14.5 = -14.5
-7y + y2 = -14.5

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = -14.5 + 12.25

Reorder the terms:
12.25 + -7y + y2 = -14.5 + 12.25

Combine like terms: -14.5 + 12.25 = -2.25
12.25 + -7y + y2 = -2.25

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = -2.25

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.

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