1y^2-28y-98=0

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Solution for 1y^2-28y-98=0 equation: 


Simplifying
1y2 + -28y + -98 = 0

Reorder the terms:
-98 + -28y + 1y2 = 0

Solving
-98 + -28y + 1y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '98' to each side of the equation.
-98 + -28y + 98 + y2 = 0 + 98

Reorder the terms:
-98 + 98 + -28y + y2 = 0 + 98

Combine like terms: -98 + 98 = 0
0 + -28y + y2 = 0 + 98
-28y + y2 = 0 + 98

Combine like terms: 0 + 98 = 98
-28y + y2 = 98

The y term is -28y.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28y + 196 + y2 = 98 + 196

Reorder the terms:
196 + -28y + y2 = 98 + 196

Combine like terms: 98 + 196 = 294
196 + -28y + y2 = 294

Factor a perfect square on the left side:
(y + -14)(y + -14) = 294

Calculate the square root of the right side: 17.146428199

Break this problem into two subproblems by setting 
(y + -14) equal to 17.146428199 and -17.146428199.


Subproblem 1
y + -14 = 17.146428199

Simplifying
y + -14 = 17.146428199

Reorder the terms:
-14 + y = 17.146428199

Solving
-14 + y = 17.146428199

Solving for variable 'y'.

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

Add '14' to each side of the equation.
-14 + 14 + y = 17.146428199 + 14

Combine like terms: -14 + 14 = 0
0 + y = 17.146428199 + 14
y = 17.146428199 + 14

Combine like terms: 17.146428199 + 14 = 31.146428199
y = 31.146428199

Simplifying
y = 31.146428199


Subproblem 2
y + -14 = -17.146428199

Simplifying
y + -14 = -17.146428199

Reorder the terms:
-14 + y = -17.146428199

Solving
-14 + y = -17.146428199

Solving for variable 'y'.

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

Add '14' to each side of the equation.
-14 + 14 + y = -17.146428199 + 14

Combine like terms: -14 + 14 = 0
0 + y = -17.146428199 + 14
y = -17.146428199 + 14

Combine like terms: -17.146428199 + 14 = -3.146428199
y = -3.146428199

Simplifying
y = -3.146428199


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {31.146428199, -3.146428199}

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