y^2+16y-262.25=0

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Solution for y^2+16y-262.25=0 equation: 


Simplifying
y2 + 16y + -262.25 = 0

Reorder the terms:
-262.25 + 16y + y2 = 0

Solving
-262.25 + 16y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '262.25' to each side of the equation.
-262.25 + 16y + 262.25 + y2 = 0 + 262.25

Reorder the terms:
-262.25 + 262.25 + 16y + y2 = 0 + 262.25

Combine like terms: -262.25 + 262.25 = 0.00
0.00 + 16y + y2 = 0 + 262.25
16y + y2 = 0 + 262.25

Combine like terms: 0 + 262.25 = 262.25
16y + y2 = 262.25

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 = 262.25 + 64

Reorder the terms:
64 + 16y + y2 = 262.25 + 64

Combine like terms: 262.25 + 64 = 326.25
64 + 16y + y2 = 326.25

Factor a perfect square on the left side:
(y + 8)(y + 8) = 326.25

Calculate the square root of the right side: 18.062391868

Break this problem into two subproblems by setting 
(y + 8) equal to 18.062391868 and -18.062391868.


Subproblem 1
y + 8 = 18.062391868

Simplifying
y + 8 = 18.062391868

Reorder the terms:
8 + y = 18.062391868

Solving
8 + y = 18.062391868

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 = 18.062391868 + -8

Combine like terms: 8 + -8 = 0
0 + y = 18.062391868 + -8
y = 18.062391868 + -8

Combine like terms: 18.062391868 + -8 = 10.062391868
y = 10.062391868

Simplifying
y = 10.062391868


Subproblem 2
y + 8 = -18.062391868

Simplifying
y + 8 = -18.062391868

Reorder the terms:
8 + y = -18.062391868

Solving
8 + y = -18.062391868

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 = -18.062391868 + -8

Combine like terms: 8 + -8 = 0
0 + y = -18.062391868 + -8
y = -18.062391868 + -8

Combine like terms: -18.062391868 + -8 = -26.062391868
y = -26.062391868

Simplifying
y = -26.062391868


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {10.062391868, -26.062391868}

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