0.5y^2-y-4=0

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Solution for 0.5y^2-y-4=0 equation: 


Simplifying
0.5y2 + -1y + -4 = 0

Reorder the terms:
-4 + -1y + 0.5y2 = 0

Solving
-4 + -1y + 0.5y2 = 0

Solving for variable 'y'.

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

Divide each side by '0.5'.
-8 + -2y + y2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -2y + 8 + y2 = 0 + 8

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

Combine like terms: -8 + 8 = 0
0 + -2y + y2 = 0 + 8
-2y + y2 = 0 + 8

Combine like terms: 0 + 8 = 8
-2y + y2 = 8

The y term is -2y.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2y + 1 + y2 = 8 + 1

Reorder the terms:
1 + -2y + y2 = 8 + 1

Combine like terms: 8 + 1 = 9
1 + -2y + y2 = 9

Factor a perfect square on the left side:
(y + -1)(y + -1) = 9

Calculate the square root of the right side: 3

Break this problem into two subproblems by setting 
(y + -1) equal to 3 and -3.


Subproblem 1
y + -1 = 3

Simplifying
y + -1 = 3

Reorder the terms:
-1 + y = 3

Solving
-1 + y = 3

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + y = 3 + 1

Combine like terms: -1 + 1 = 0
0 + y = 3 + 1
y = 3 + 1

Combine like terms: 3 + 1 = 4
y = 4

Simplifying
y = 4


Subproblem 2
y + -1 = -3

Simplifying
y + -1 = -3

Reorder the terms:
-1 + y = -3

Solving
-1 + y = -3

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + y = -3 + 1

Combine like terms: -1 + 1 = 0
0 + y = -3 + 1
y = -3 + 1

Combine like terms: -3 + 1 = -2
y = -2

Simplifying
y = -2


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4, -2}

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