(5y^2+1)-(y^2-4y-8)=

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Solution for (5y^2+1)-(y^2-4y-8)= equation: 


Simplifying
(5y2 + 1) + -1(y2 + -4y + -8) = 0

Reorder the terms:
(1 + 5y2) + -1(y2 + -4y + -8) = 0

Remove parenthesis around (1 + 5y2)
1 + 5y2 + -1(y2 + -4y + -8) = 0

Reorder the terms:
1 + 5y2 + -1(-8 + -4y + y2) = 0
1 + 5y2 + (-8 * -1 + -4y * -1 + y2 * -1) = 0
1 + 5y2 + (8 + 4y + -1y2) = 0

Reorder the terms:
1 + 8 + 4y + 5y2 + -1y2 = 0

Combine like terms: 1 + 8 = 9
9 + 4y + 5y2 + -1y2 = 0

Combine like terms: 5y2 + -1y2 = 4y2
9 + 4y + 4y2 = 0

Solving
9 + 4y + 4y2 = 0

Solving for variable 'y'.

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

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

Move the constant term to the right:

Add '-2.25' to each side of the equation.
2.25 + y + -2.25 + y2 = 0 + -2.25

Reorder the terms:
2.25 + -2.25 + y + y2 = 0 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + y + y2 = 0 + -2.25
y + y2 = 0 + -2.25

Combine like terms: 0 + -2.25 = -2.25
y + y2 = -2.25

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + y2 = -2.25 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = -2.25 + 0.25

Combine like terms: -2.25 + 0.25 = -2
1.25 + y2 = -2

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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