y^2+2y-263=0

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Solution for y^2+2y-263=0 equation: 


Simplifying
y2 + 2y + -263 = 0

Reorder the terms:
-263 + 2y + y2 = 0

Solving
-263 + 2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '263' to each side of the equation.
-263 + 2y + 263 + y2 = 0 + 263

Reorder the terms:
-263 + 263 + 2y + y2 = 0 + 263

Combine like terms: -263 + 263 = 0
0 + 2y + y2 = 0 + 263
2y + y2 = 0 + 263

Combine like terms: 0 + 263 = 263
2y + y2 = 263

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = 263 + 1

Reorder the terms:
1 + 2y + y2 = 263 + 1

Combine like terms: 263 + 1 = 264
1 + 2y + y2 = 264

Factor a perfect square on the left side:
(y + 1)(y + 1) = 264

Calculate the square root of the right side: 16.248076809

Break this problem into two subproblems by setting 
(y + 1) equal to 16.248076809 and -16.248076809.


Subproblem 1
y + 1 = 16.248076809

Simplifying
y + 1 = 16.248076809

Reorder the terms:
1 + y = 16.248076809

Solving
1 + y = 16.248076809

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 16.248076809 + -1

Combine like terms: 1 + -1 = 0
0 + y = 16.248076809 + -1
y = 16.248076809 + -1

Combine like terms: 16.248076809 + -1 = 15.248076809
y = 15.248076809

Simplifying
y = 15.248076809


Subproblem 2
y + 1 = -16.248076809

Simplifying
y + 1 = -16.248076809

Reorder the terms:
1 + y = -16.248076809

Solving
1 + y = -16.248076809

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -16.248076809 + -1

Combine like terms: 1 + -1 = 0
0 + y = -16.248076809 + -1
y = -16.248076809 + -1

Combine like terms: -16.248076809 + -1 = -17.248076809
y = -17.248076809

Simplifying
y = -17.248076809


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {15.248076809, -17.248076809}

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