-2y^2-9y=-10

Solution for -2y^2-9y=-10 equation:

Simplifying
-2y2 + -9y = -10

Reorder the terms:
-9y + -2y2 = -10

Solving
-9y + -2y2 = -10

Solving for variable 'y'.

Reorder the terms:
10 + -9y + -2y2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -9y + -2y2 = 0

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

Divide each side by '-2'.
-5 + 4.5y + y2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 4.5y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + 4.5y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4.5y + y2 = 0 + 5
4.5y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
4.5y + y2 = 5

The y term is 4.5y.  Take half its coefficient (2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
4.5y + 5.0625 + y2 = 5 + 5.0625

Reorder the terms:
5.0625 + 4.5y + y2 = 5 + 5.0625

Combine like terms: 5 + 5.0625 = 10.0625
5.0625 + 4.5y + y2 = 10.0625

Factor a perfect square on the left side:
(y + 2.25)(y + 2.25) = 10.0625

Calculate the square root of the right side: 3.172144385

Break this problem into two subproblems by setting 
(y + 2.25) equal to 3.172144385 and -3.172144385.

Subproblem 1
y + 2.25 = 3.172144385

Simplifying
y + 2.25 = 3.172144385

Reorder the terms:
2.25 + y = 3.172144385

Solving
2.25 + y = 3.172144385

Solving for variable 'y'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + y = 3.172144385 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + y = 3.172144385 + -2.25
y = 3.172144385 + -2.25

Combine like terms: 3.172144385 + -2.25 = 0.922144385
y = 0.922144385

Simplifying
y = 0.922144385

Subproblem 2
y + 2.25 = -3.172144385

Simplifying
y + 2.25 = -3.172144385

Reorder the terms:
2.25 + y = -3.172144385

Solving
2.25 + y = -3.172144385

Solving for variable 'y'.

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

Add '-2.25' to each side of the equation.
2.25 + -2.25 + y = -3.172144385 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + y = -3.172144385 + -2.25
y = -3.172144385 + -2.25

Combine like terms: -3.172144385 + -2.25 = -5.422144385
y = -5.422144385

Simplifying
y = -5.422144385

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.922144385, -5.422144385}