2y^2+8y+31=0

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Solution for 2y^2+8y+31=0 equation:


Simplifying
2y2 + 8y + 31 = 0

Reorder the terms:
31 + 8y + 2y2 = 0

Solving
31 + 8y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
15.5 + 4y + y2 = 0

Move the constant term to the right:

Add '-15.5' to each side of the equation.
15.5 + 4y + -15.5 + y2 = 0 + -15.5

Reorder the terms:
15.5 + -15.5 + 4y + y2 = 0 + -15.5

Combine like terms: 15.5 + -15.5 = 0.0
0.0 + 4y + y2 = 0 + -15.5
4y + y2 = 0 + -15.5

Combine like terms: 0 + -15.5 = -15.5
4y + y2 = -15.5

The y term is 4y.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4y + 4 + y2 = -15.5 + 4

Reorder the terms:
4 + 4y + y2 = -15.5 + 4

Combine like terms: -15.5 + 4 = -11.5
4 + 4y + y2 = -11.5

Factor a perfect square on the left side:
(y + 2)(y + 2) = -11.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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