y^2+2y-71=0

Solution for y^2+2y-71=0 equation:

Simplifying
y2 + 2y + -71 = 0

Reorder the terms:
-71 + 2y + y2 = 0

Solving
-71 + 2y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '71' to each side of the equation.
-71 + 2y + 71 + y2 = 0 + 71

Reorder the terms:
-71 + 71 + 2y + y2 = 0 + 71

Combine like terms: -71 + 71 = 0
0 + 2y + y2 = 0 + 71
2y + y2 = 0 + 71

Combine like terms: 0 + 71 = 71
2y + y2 = 71

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 = 71 + 1

Reorder the terms:
1 + 2y + y2 = 71 + 1

Combine like terms: 71 + 1 = 72
1 + 2y + y2 = 72

Factor a perfect square on the left side:
(y + 1)(y + 1) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(y + 1) equal to 8.485281374 and -8.485281374.

Subproblem 1
y + 1 = 8.485281374

Simplifying
y + 1 = 8.485281374

Reorder the terms:
1 + y = 8.485281374

Solving
1 + y = 8.485281374

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 = 8.485281374 + -1

Combine like terms: 1 + -1 = 0
0 + y = 8.485281374 + -1
y = 8.485281374 + -1

Combine like terms: 8.485281374 + -1 = 7.485281374
y = 7.485281374

Simplifying
y = 7.485281374

Subproblem 2
y + 1 = -8.485281374

Simplifying
y + 1 = -8.485281374

Reorder the terms:
1 + y = -8.485281374

Solving
1 + y = -8.485281374

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 = -8.485281374 + -1

Combine like terms: 1 + -1 = 0
0 + y = -8.485281374 + -1
y = -8.485281374 + -1

Combine like terms: -8.485281374 + -1 = -9.485281374
y = -9.485281374

Simplifying
y = -9.485281374

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {7.485281374, -9.485281374}