-11=y^2-13y+24

Solution for -11=y^2-13y+24 equation:

Simplifying
-11 = y2 + -13y + 24

Reorder the terms:
-11 = 24 + -13y + y2

Solving
-11 = 24 + -13y + y2

Solving for variable 'y'.

Combine like terms: -11 + -24 = -35
-35 + 13y + -1y2 = 24 + -13y + y2 + -24 + 13y + -1y2

Reorder the terms:
-35 + 13y + -1y2 = 24 + -24 + -13y + 13y + y2 + -1y2

Combine like terms: 24 + -24 = 0
-35 + 13y + -1y2 = 0 + -13y + 13y + y2 + -1y2
-35 + 13y + -1y2 = -13y + 13y + y2 + -1y2

Combine like terms: -13y + 13y = 0
-35 + 13y + -1y2 = 0 + y2 + -1y2
-35 + 13y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-35 + 13y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
35 + -13y + y2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -13y + -35 + y2 = 0 + -35

Reorder the terms:
35 + -35 + -13y + y2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -13y + y2 = 0 + -35
-13y + y2 = 0 + -35

Combine like terms: 0 + -35 = -35
-13y + y2 = -35

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 = -35 + 42.25

Reorder the terms:
42.25 + -13y + y2 = -35 + 42.25

Combine like terms: -35 + 42.25 = 7.25
42.25 + -13y + y2 = 7.25

Factor a perfect square on the left side:
(y + -6.5)(y + -6.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(y + -6.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
y + -6.5 = 2.692582404

Simplifying
y + -6.5 = 2.692582404

Reorder the terms:
-6.5 + y = 2.692582404

Solving
-6.5 + y = 2.692582404

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 = 2.692582404 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = 2.692582404 + 6.5
y = 2.692582404 + 6.5

Combine like terms: 2.692582404 + 6.5 = 9.192582404
y = 9.192582404

Simplifying
y = 9.192582404

Subproblem 2
y + -6.5 = -2.692582404

Simplifying
y + -6.5 = -2.692582404

Reorder the terms:
-6.5 + y = -2.692582404

Solving
-6.5 + y = -2.692582404

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 = -2.692582404 + 6.5

Combine like terms: -6.5 + 6.5 = 0.0
0.0 + y = -2.692582404 + 6.5
y = -2.692582404 + 6.5

Combine like terms: -2.692582404 + 6.5 = 3.807417596
y = 3.807417596

Simplifying
y = 3.807417596

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {9.192582404, 3.807417596}