2y^2-14y-1=-16y

Solution for 2y^2-14y-1=-16y equation:

Simplifying
2y2 + -14y + -1 = -16y

Reorder the terms:
-1 + -14y + 2y2 = -16y

Solving
-1 + -14y + 2y2 = -16y

Solving for variable 'y'.

Reorder the terms:
-1 + -14y + 16y + 2y2 = -16y + 16y

Combine like terms: -14y + 16y = 2y
-1 + 2y + 2y2 = -16y + 16y

Combine like terms: -16y + 16y = 0
-1 + 2y + 2y2 = 0

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

Divide each side by '2'.
-0.5 + y + y2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + y + 0.5 + y2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + y + y2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y + y2 = 0 + 0.5
y + y2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
y + y2 = 0.5

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + y2 = 0.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
1.25 + y2 = 0.75

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(y + 0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1
y + 0.5 = 0.866025404

Simplifying
y + 0.5 = 0.866025404

Reorder the terms:
0.5 + y = 0.866025404

Solving
0.5 + y = 0.866025404

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 0.866025404 + -0.5
y = 0.866025404 + -0.5

Combine like terms: 0.866025404 + -0.5 = 0.366025404
y = 0.366025404

Simplifying
y = 0.366025404

Subproblem 2
y + 0.5 = -0.866025404

Simplifying
y + 0.5 = -0.866025404

Reorder the terms:
0.5 + y = -0.866025404

Solving
0.5 + y = -0.866025404

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -0.866025404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -0.866025404 + -0.5
y = -0.866025404 + -0.5

Combine like terms: -0.866025404 + -0.5 = -1.366025404
y = -1.366025404

Simplifying
y = -1.366025404

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.366025404, -1.366025404}