2y^2+5y-2=0

Solution for 2y^2+5y-2=0 equation:

Simplifying
2y2 + 5y + -2 = 0

Reorder the terms:
-2 + 5y + 2y2 = 0

Solving
-2 + 5y + 2y2 = 0

Solving for variable 'y'.

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

Divide each side by '2'.
-1 + 2.5y + y2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.5y + 1 + y2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.5y + y2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.5y + y2 = 0 + 1
2.5y + y2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.5y + y2 = 1

The y term is 2.5y.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5y + 1.5625 + y2 = 1 + 1.5625

Reorder the terms:
1.5625 + 2.5y + y2 = 1 + 1.5625

Combine like terms: 1 + 1.5625 = 2.5625
1.5625 + 2.5y + y2 = 2.5625

Factor a perfect square on the left side:
(y + 1.25)(y + 1.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(y + 1.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
y + 1.25 = 1.600781059

Simplifying
y + 1.25 = 1.600781059

Reorder the terms:
1.25 + y = 1.600781059

Solving
1.25 + y = 1.600781059

Solving for variable 'y'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + y = 1.600781059 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + y = 1.600781059 + -1.25
y = 1.600781059 + -1.25

Combine like terms: 1.600781059 + -1.25 = 0.350781059
y = 0.350781059

Simplifying
y = 0.350781059

Subproblem 2
y + 1.25 = -1.600781059

Simplifying
y + 1.25 = -1.600781059

Reorder the terms:
1.25 + y = -1.600781059

Solving
1.25 + y = -1.600781059

Solving for variable 'y'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + y = -1.600781059 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + y = -1.600781059 + -1.25
y = -1.600781059 + -1.25

Combine like terms: -1.600781059 + -1.25 = -2.850781059
y = -2.850781059

Simplifying
y = -2.850781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.350781059, -2.850781059}