y^2-9.5y-16.5=0

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Solution for y^2-9.5y-16.5=0 equation: 


Simplifying
y2 + -9.5y + -16.5 = 0

Reorder the terms:
-16.5 + -9.5y + y2 = 0

Solving
-16.5 + -9.5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '16.5' to each side of the equation.
-16.5 + -9.5y + 16.5 + y2 = 0 + 16.5

Reorder the terms:
-16.5 + 16.5 + -9.5y + y2 = 0 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + -9.5y + y2 = 0 + 16.5
-9.5y + y2 = 0 + 16.5

Combine like terms: 0 + 16.5 = 16.5
-9.5y + y2 = 16.5

The y term is -9.5y.  Take half its coefficient (-4.75).
Square it (22.5625) and add it to both sides.

Add '22.5625' to each side of the equation.
-9.5y + 22.5625 + y2 = 16.5 + 22.5625

Reorder the terms:
22.5625 + -9.5y + y2 = 16.5 + 22.5625

Combine like terms: 16.5 + 22.5625 = 39.0625
22.5625 + -9.5y + y2 = 39.0625

Factor a perfect square on the left side:
(y + -4.75)(y + -4.75) = 39.0625

Calculate the square root of the right side: 6.25

Break this problem into two subproblems by setting 
(y + -4.75) equal to 6.25 and -6.25.


Subproblem 1
y + -4.75 = 6.25

Simplifying
y + -4.75 = 6.25

Reorder the terms:
-4.75 + y = 6.25

Solving
-4.75 + y = 6.25

Solving for variable 'y'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + y = 6.25 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + y = 6.25 + 4.75
y = 6.25 + 4.75

Combine like terms: 6.25 + 4.75 = 11
y = 11

Simplifying
y = 11


Subproblem 2
y + -4.75 = -6.25

Simplifying
y + -4.75 = -6.25

Reorder the terms:
-4.75 + y = -6.25

Solving
-4.75 + y = -6.25

Solving for variable 'y'.

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

Add '4.75' to each side of the equation.
-4.75 + 4.75 + y = -6.25 + 4.75

Combine like terms: -4.75 + 4.75 = 0.00
0.00 + y = -6.25 + 4.75
y = -6.25 + 4.75

Combine like terms: -6.25 + 4.75 = -1.5
y = -1.5

Simplifying
y = -1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11, -1.5}

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