y^2-16y-198=0

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Solution for y^2-16y-198=0 equation: 


Simplifying
y2 + -16y + -198 = 0

Reorder the terms:
-198 + -16y + y2 = 0

Solving
-198 + -16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '198' to each side of the equation.
-198 + -16y + 198 + y2 = 0 + 198

Reorder the terms:
-198 + 198 + -16y + y2 = 0 + 198

Combine like terms: -198 + 198 = 0
0 + -16y + y2 = 0 + 198
-16y + y2 = 0 + 198

Combine like terms: 0 + 198 = 198
-16y + y2 = 198

The y term is -16y.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16y + 64 + y2 = 198 + 64

Reorder the terms:
64 + -16y + y2 = 198 + 64

Combine like terms: 198 + 64 = 262
64 + -16y + y2 = 262

Factor a perfect square on the left side:
(y + -8)(y + -8) = 262

Calculate the square root of the right side: 16.186414056

Break this problem into two subproblems by setting 
(y + -8) equal to 16.186414056 and -16.186414056.


Subproblem 1
y + -8 = 16.186414056

Simplifying
y + -8 = 16.186414056

Reorder the terms:
-8 + y = 16.186414056

Solving
-8 + y = 16.186414056

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = 16.186414056 + 8

Combine like terms: -8 + 8 = 0
0 + y = 16.186414056 + 8
y = 16.186414056 + 8

Combine like terms: 16.186414056 + 8 = 24.186414056
y = 24.186414056

Simplifying
y = 24.186414056


Subproblem 2
y + -8 = -16.186414056

Simplifying
y + -8 = -16.186414056

Reorder the terms:
-8 + y = -16.186414056

Solving
-8 + y = -16.186414056

Solving for variable 'y'.

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

Add '8' to each side of the equation.
-8 + 8 + y = -16.186414056 + 8

Combine like terms: -8 + 8 = 0
0 + y = -16.186414056 + 8
y = -16.186414056 + 8

Combine like terms: -16.186414056 + 8 = -8.186414056
y = -8.186414056

Simplifying
y = -8.186414056


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {24.186414056, -8.186414056}

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