y^2+8y-215=0

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Solution for y^2+8y-215=0 equation: 


Simplifying
y2 + 8y + -215 = 0

Reorder the terms:
-215 + 8y + y2 = 0

Solving
-215 + 8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '215' to each side of the equation.
-215 + 8y + 215 + y2 = 0 + 215

Reorder the terms:
-215 + 215 + 8y + y2 = 0 + 215

Combine like terms: -215 + 215 = 0
0 + 8y + y2 = 0 + 215
8y + y2 = 0 + 215

Combine like terms: 0 + 215 = 215
8y + y2 = 215

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 = 215 + 16

Reorder the terms:
16 + 8y + y2 = 215 + 16

Combine like terms: 215 + 16 = 231
16 + 8y + y2 = 231

Factor a perfect square on the left side:
(y + 4)(y + 4) = 231

Calculate the square root of the right side: 15.198684154

Break this problem into two subproblems by setting 
(y + 4) equal to 15.198684154 and -15.198684154.


Subproblem 1
y + 4 = 15.198684154

Simplifying
y + 4 = 15.198684154

Reorder the terms:
4 + y = 15.198684154

Solving
4 + y = 15.198684154

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 = 15.198684154 + -4

Combine like terms: 4 + -4 = 0
0 + y = 15.198684154 + -4
y = 15.198684154 + -4

Combine like terms: 15.198684154 + -4 = 11.198684154
y = 11.198684154

Simplifying
y = 11.198684154


Subproblem 2
y + 4 = -15.198684154

Simplifying
y + 4 = -15.198684154

Reorder the terms:
4 + y = -15.198684154

Solving
4 + y = -15.198684154

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 = -15.198684154 + -4

Combine like terms: 4 + -4 = 0
0 + y = -15.198684154 + -4
y = -15.198684154 + -4

Combine like terms: -15.198684154 + -4 = -19.198684154
y = -19.198684154

Simplifying
y = -19.198684154


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {11.198684154, -19.198684154}

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