2y^2-8=-7y

Solution for 2y^2-8=-7y equation:

Simplifying
2y2 + -8 = -7y

Reorder the terms:
-8 + 2y2 = -7y

Solving
-8 + 2y2 = -7y

Solving for variable 'y'.

Reorder the terms:
-8 + 7y + 2y2 = -7y + 7y

Combine like terms: -7y + 7y = 0
-8 + 7y + 2y2 = 0

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

Divide each side by '2'.
-4 + 3.5y + y2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 3.5y + 4 + y2 = 0 + 4

Reorder the terms:
-4 + 4 + 3.5y + y2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3.5y + y2 = 0 + 4
3.5y + y2 = 0 + 4

Combine like terms: 0 + 4 = 4
3.5y + y2 = 4

The y term is 3.5y.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5y + 3.0625 + y2 = 4 + 3.0625

Reorder the terms:
3.0625 + 3.5y + y2 = 4 + 3.0625

Combine like terms: 4 + 3.0625 = 7.0625
3.0625 + 3.5y + y2 = 7.0625

Factor a perfect square on the left side:
(y + 1.75)(y + 1.75) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(y + 1.75) equal to 2.657536453 and -2.657536453.

Subproblem 1
y + 1.75 = 2.657536453

Simplifying
y + 1.75 = 2.657536453

Reorder the terms:
1.75 + y = 2.657536453

Solving
1.75 + y = 2.657536453

Solving for variable 'y'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + y = 2.657536453 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + y = 2.657536453 + -1.75
y = 2.657536453 + -1.75

Combine like terms: 2.657536453 + -1.75 = 0.907536453
y = 0.907536453

Simplifying
y = 0.907536453

Subproblem 2
y + 1.75 = -2.657536453

Simplifying
y + 1.75 = -2.657536453

Reorder the terms:
1.75 + y = -2.657536453

Solving
1.75 + y = -2.657536453

Solving for variable 'y'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + y = -2.657536453 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + y = -2.657536453 + -1.75
y = -2.657536453 + -1.75

Combine like terms: -2.657536453 + -1.75 = -4.407536453
y = -4.407536453

Simplifying
y = -4.407536453

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.907536453, -4.407536453}