0.5y^2+2.5y-98=0

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Solution for 0.5y^2+2.5y-98=0 equation: 


Simplifying
0.5y2 + 2.5y + -98 = 0

Reorder the terms:
-98 + 2.5y + 0.5y2 = 0

Solving
-98 + 2.5y + 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'.
-196 + 5y + y2 = 0

Move the constant term to the right:

Add '196' to each side of the equation.
-196 + 5y + 196 + y2 = 0 + 196

Reorder the terms:
-196 + 196 + 5y + y2 = 0 + 196

Combine like terms: -196 + 196 = 0
0 + 5y + y2 = 0 + 196
5y + y2 = 0 + 196

Combine like terms: 0 + 196 = 196
5y + y2 = 196

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 196 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 196 + 6.25

Combine like terms: 196 + 6.25 = 202.25
6.25 + 5y + y2 = 202.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 202.25

Calculate the square root of the right side: 14.221462653

Break this problem into two subproblems by setting 
(y + 2.5) equal to 14.221462653 and -14.221462653.


Subproblem 1
y + 2.5 = 14.221462653

Simplifying
y + 2.5 = 14.221462653

Reorder the terms:
2.5 + y = 14.221462653

Solving
2.5 + y = 14.221462653

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 14.221462653 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 14.221462653 + -2.5
y = 14.221462653 + -2.5

Combine like terms: 14.221462653 + -2.5 = 11.721462653
y = 11.721462653

Simplifying
y = 11.721462653


Subproblem 2
y + 2.5 = -14.221462653

Simplifying
y + 2.5 = -14.221462653

Reorder the terms:
2.5 + y = -14.221462653

Solving
2.5 + y = -14.221462653

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -14.221462653 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -14.221462653 + -2.5
y = -14.221462653 + -2.5

Combine like terms: -14.221462653 + -2.5 = -16.721462653
y = -16.721462653

Simplifying
y = -16.721462653


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.721462653, -16.721462653}

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