2y^2-98y-80=0

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Solution for 2y^2-98y-80=0 equation: 


Simplifying
2y2 + -98y + -80 = 0

Reorder the terms:
-80 + -98y + 2y2 = 0

Solving
-80 + -98y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -49y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-40 + -49y + y2)' equal to zero and attempt to solve:

Simplifying
-40 + -49y + y2 = 0

Solving
-40 + -49y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -49y + 40 + y2 = 0 + 40

Reorder the terms:
-40 + 40 + -49y + y2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -49y + y2 = 0 + 40
-49y + y2 = 0 + 40

Combine like terms: 0 + 40 = 40
-49y + y2 = 40

The y term is -49y.  Take half its coefficient (-24.5).
Square it (600.25) and add it to both sides.

Add '600.25' to each side of the equation.
-49y + 600.25 + y2 = 40 + 600.25

Reorder the terms:
600.25 + -49y + y2 = 40 + 600.25

Combine like terms: 40 + 600.25 = 640.25
600.25 + -49y + y2 = 640.25

Factor a perfect square on the left side:
(y + -24.5)(y + -24.5) = 640.25

Calculate the square root of the right side: 25.303161858

Break this problem into two subproblems by setting 
(y + -24.5) equal to 25.303161858 and -25.303161858.


Subproblem 1
y + -24.5 = 25.303161858

Simplifying
y + -24.5 = 25.303161858

Reorder the terms:
-24.5 + y = 25.303161858

Solving
-24.5 + y = 25.303161858

Solving for variable 'y'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + y = 25.303161858 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + y = 25.303161858 + 24.5
y = 25.303161858 + 24.5

Combine like terms: 25.303161858 + 24.5 = 49.803161858
y = 49.803161858

Simplifying
y = 49.803161858


Subproblem 2
y + -24.5 = -25.303161858

Simplifying
y + -24.5 = -25.303161858

Reorder the terms:
-24.5 + y = -25.303161858

Solving
-24.5 + y = -25.303161858

Solving for variable 'y'.

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

Add '24.5' to each side of the equation.
-24.5 + 24.5 + y = -25.303161858 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + y = -25.303161858 + 24.5
y = -25.303161858 + 24.5

Combine like terms: -25.303161858 + 24.5 = -0.803161858
y = -0.803161858

Simplifying
y = -0.803161858


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {49.803161858, -0.803161858}
Solution
y = {49.803161858, -0.803161858}

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