y^2+13y-57=0

Solution for y^2+13y-57=0 equation:

Simplifying
y2 + 13y + -57 = 0

Reorder the terms:
-57 + 13y + y2 = 0

Solving
-57 + 13y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '57' to each side of the equation.
-57 + 13y + 57 + y2 = 0 + 57

Reorder the terms:
-57 + 57 + 13y + y2 = 0 + 57

Combine like terms: -57 + 57 = 0
0 + 13y + y2 = 0 + 57
13y + y2 = 0 + 57

Combine like terms: 0 + 57 = 57
13y + y2 = 57

The y term is 13y.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13y + 42.25 + y2 = 57 + 42.25

Reorder the terms:
42.25 + 13y + y2 = 57 + 42.25

Combine like terms: 57 + 42.25 = 99.25
42.25 + 13y + y2 = 99.25

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = 99.25

Calculate the square root of the right side: 9.962429423

Break this problem into two subproblems by setting 
(y + 6.5) equal to 9.962429423 and -9.962429423.

Subproblem 1
y + 6.5 = 9.962429423

Simplifying
y + 6.5 = 9.962429423

Reorder the terms:
6.5 + y = 9.962429423

Solving
6.5 + y = 9.962429423

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = 9.962429423 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 9.962429423 + -6.5
y = 9.962429423 + -6.5

Combine like terms: 9.962429423 + -6.5 = 3.462429423
y = 3.462429423

Simplifying
y = 3.462429423

Subproblem 2
y + 6.5 = -9.962429423

Simplifying
y + 6.5 = -9.962429423

Reorder the terms:
6.5 + y = -9.962429423

Solving
6.5 + y = -9.962429423

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = -9.962429423 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = -9.962429423 + -6.5
y = -9.962429423 + -6.5

Combine like terms: -9.962429423 + -6.5 = -16.462429423
y = -16.462429423

Simplifying
y = -16.462429423

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.462429423, -16.462429423}