10y^2+11y-6=5

Solution for 10y^2+11y-6=5 equation:

Simplifying
10y2 + 11y + -6 = 5

Reorder the terms:
-6 + 11y + 10y2 = 5

Solving
-6 + 11y + 10y2 = 5

Solving for variable 'y'.

Reorder the terms:
-6 + -5 + 11y + 10y2 = 5 + -5

Combine like terms: -6 + -5 = -11
-11 + 11y + 10y2 = 5 + -5

Combine like terms: 5 + -5 = 0
-11 + 11y + 10y2 = 0

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

Divide each side by '10'.
-1.1 + 1.1y + y2 = 0

Move the constant term to the right:

Add '1.1' to each side of the equation.
-1.1 + 1.1y + 1.1 + y2 = 0 + 1.1

Reorder the terms:
-1.1 + 1.1 + 1.1y + y2 = 0 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + 1.1y + y2 = 0 + 1.1
1.1y + y2 = 0 + 1.1

Combine like terms: 0 + 1.1 = 1.1
1.1y + y2 = 1.1

The y term is 1.1y.  Take half its coefficient (0.55).
Square it (0.3025) and add it to both sides.

Add '0.3025' to each side of the equation.
1.1y + 0.3025 + y2 = 1.1 + 0.3025

Reorder the terms:
0.3025 + 1.1y + y2 = 1.1 + 0.3025

Combine like terms: 1.1 + 0.3025 = 1.4025
0.3025 + 1.1y + y2 = 1.4025

Factor a perfect square on the left side:
(y + 0.55)(y + 0.55) = 1.4025

Calculate the square root of the right side: 1.184271928

Break this problem into two subproblems by setting 
(y + 0.55) equal to 1.184271928 and -1.184271928.

Subproblem 1
y + 0.55 = 1.184271928

Simplifying
y + 0.55 = 1.184271928

Reorder the terms:
0.55 + y = 1.184271928

Solving
0.55 + y = 1.184271928

Solving for variable 'y'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + y = 1.184271928 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + y = 1.184271928 + -0.55
y = 1.184271928 + -0.55

Combine like terms: 1.184271928 + -0.55 = 0.634271928
y = 0.634271928

Simplifying
y = 0.634271928

Subproblem 2
y + 0.55 = -1.184271928

Simplifying
y + 0.55 = -1.184271928

Reorder the terms:
0.55 + y = -1.184271928

Solving
0.55 + y = -1.184271928

Solving for variable 'y'.

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

Add '-0.55' to each side of the equation.
0.55 + -0.55 + y = -1.184271928 + -0.55

Combine like terms: 0.55 + -0.55 = 0.00
0.00 + y = -1.184271928 + -0.55
y = -1.184271928 + -0.55

Combine like terms: -1.184271928 + -0.55 = -1.734271928
y = -1.734271928

Simplifying
y = -1.734271928

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.634271928, -1.734271928}