y^2+16y-1.5=0

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Solution for y^2+16y-1.5=0 equation: 


Simplifying
y2 + 16y + -1.5 = 0

Reorder the terms:
-1.5 + 16y + y2 = 0

Solving
-1.5 + 16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 16y + 1.5 + y2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 16y + y2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 16y + y2 = 0 + 1.5
16y + y2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
16y + y2 = 1.5

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 = 1.5 + 64

Reorder the terms:
64 + 16y + y2 = 1.5 + 64

Combine like terms: 1.5 + 64 = 65.5
64 + 16y + y2 = 65.5

Factor a perfect square on the left side:
(y + 8)(y + 8) = 65.5

Calculate the square root of the right side: 8.093207028

Break this problem into two subproblems by setting 
(y + 8) equal to 8.093207028 and -8.093207028.


Subproblem 1
y + 8 = 8.093207028

Simplifying
y + 8 = 8.093207028

Reorder the terms:
8 + y = 8.093207028

Solving
8 + y = 8.093207028

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 = 8.093207028 + -8

Combine like terms: 8 + -8 = 0
0 + y = 8.093207028 + -8
y = 8.093207028 + -8

Combine like terms: 8.093207028 + -8 = 0.093207028
y = 0.093207028

Simplifying
y = 0.093207028


Subproblem 2
y + 8 = -8.093207028

Simplifying
y + 8 = -8.093207028

Reorder the terms:
8 + y = -8.093207028

Solving
8 + y = -8.093207028

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 = -8.093207028 + -8

Combine like terms: 8 + -8 = 0
0 + y = -8.093207028 + -8
y = -8.093207028 + -8

Combine like terms: -8.093207028 + -8 = -16.093207028
y = -16.093207028

Simplifying
y = -16.093207028


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.093207028, -16.093207028}

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