2y^2-16y-98=0

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Solution for 2y^2-16y-98=0 equation: 


Simplifying
2y2 + -16y + -98 = 0

Reorder the terms:
-98 + -16y + 2y2 = 0

Solving
-98 + -16y + 2y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-49 + -8y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-49 + -8y + y2)' equal to zero and attempt to solve:

Simplifying
-49 + -8y + y2 = 0

Solving
-49 + -8y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '49' to each side of the equation.
-49 + -8y + 49 + y2 = 0 + 49

Reorder the terms:
-49 + 49 + -8y + y2 = 0 + 49

Combine like terms: -49 + 49 = 0
0 + -8y + y2 = 0 + 49
-8y + y2 = 0 + 49

Combine like terms: 0 + 49 = 49
-8y + y2 = 49

The y term is -8y.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8y + 16 + y2 = 49 + 16

Reorder the terms:
16 + -8y + y2 = 49 + 16

Combine like terms: 49 + 16 = 65
16 + -8y + y2 = 65

Factor a perfect square on the left side:
(y + -4)(y + -4) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(y + -4) equal to 8.062257748 and -8.062257748.


Subproblem 1
y + -4 = 8.062257748

Simplifying
y + -4 = 8.062257748

Reorder the terms:
-4 + y = 8.062257748

Solving
-4 + y = 8.062257748

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = 8.062257748 + 4

Combine like terms: -4 + 4 = 0
0 + y = 8.062257748 + 4
y = 8.062257748 + 4

Combine like terms: 8.062257748 + 4 = 12.062257748
y = 12.062257748

Simplifying
y = 12.062257748


Subproblem 2
y + -4 = -8.062257748

Simplifying
y + -4 = -8.062257748

Reorder the terms:
-4 + y = -8.062257748

Solving
-4 + y = -8.062257748

Solving for variable 'y'.

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

Add '4' to each side of the equation.
-4 + 4 + y = -8.062257748 + 4

Combine like terms: -4 + 4 = 0
0 + y = -8.062257748 + 4
y = -8.062257748 + 4

Combine like terms: -8.062257748 + 4 = -4.062257748
y = -4.062257748

Simplifying
y = -4.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {12.062257748, -4.062257748}
Solution
y = {12.062257748, -4.062257748}

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