y^2+0.8y+0.15=0

Solution for y^2+0.8y+0.15=0 equation:

Simplifying
y2 + 0.8y + 0.15 = 0

Reorder the terms:
0.15 + 0.8y + y2 = 0

Solving
0.15 + 0.8y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-0.15' to each side of the equation.
0.15 + 0.8y + -0.15 + y2 = 0 + -0.15

Reorder the terms:
0.15 + -0.15 + 0.8y + y2 = 0 + -0.15

Combine like terms: 0.15 + -0.15 = 0.00
0.00 + 0.8y + y2 = 0 + -0.15
0.8y + y2 = 0 + -0.15

Combine like terms: 0 + -0.15 = -0.15
0.8y + y2 = -0.15

The y term is 0.8y.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8y + 0.16 + y2 = -0.15 + 0.16

Reorder the terms:
0.16 + 0.8y + y2 = -0.15 + 0.16

Combine like terms: -0.15 + 0.16 = 0.01
0.16 + 0.8y + y2 = 0.01

Factor a perfect square on the left side:
(y + 0.4)(y + 0.4) = 0.01

Calculate the square root of the right side: 0.1

Break this problem into two subproblems by setting 
(y + 0.4) equal to 0.1 and -0.1.

Subproblem 1
y + 0.4 = 0.1

Simplifying
y + 0.4 = 0.1

Reorder the terms:
0.4 + y = 0.1

Solving
0.4 + y = 0.1

Solving for variable 'y'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + y = 0.1 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + y = 0.1 + -0.4
y = 0.1 + -0.4

Combine like terms: 0.1 + -0.4 = -0.3
y = -0.3

Simplifying
y = -0.3

Subproblem 2
y + 0.4 = -0.1

Simplifying
y + 0.4 = -0.1

Reorder the terms:
0.4 + y = -0.1

Solving
0.4 + y = -0.1

Solving for variable 'y'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + y = -0.1 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + y = -0.1 + -0.4
y = -0.1 + -0.4

Combine like terms: -0.1 + -0.4 = -0.5
y = -0.5

Simplifying
y = -0.5

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.3, -0.5}