y^2+0.1y+.0025=0

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Solution for y^2+0.1y+.0025=0 equation: 


Simplifying
y2 + 0.1y + 0.0025 = 0

Reorder the terms:
0.0025 + 0.1y + y2 = 0

Solving
0.0025 + 0.1y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-0.0025' to each side of the equation.
0.0025 + 0.1y + -0.0025 + y2 = 0 + -0.0025

Reorder the terms:
0.0025 + -0.0025 + 0.1y + y2 = 0 + -0.0025

Combine like terms: 0.0025 + -0.0025 = 0.0000
0.0000 + 0.1y + y2 = 0 + -0.0025
0.1y + y2 = 0 + -0.0025

Combine like terms: 0 + -0.0025 = -0.0025
0.1y + y2 = -0.0025

The y term is 0.1y.  Take half its coefficient (0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
0.1y + 0.0025 + y2 = -0.0025 + 0.0025

Reorder the terms:
0.0025 + 0.1y + y2 = -0.0025 + 0.0025

Combine like terms: -0.0025 + 0.0025 = 0.0000
0.0025 + 0.1y + y2 = 0.0000

Factor a perfect square on the left side:
(y + 0.05)(y + 0.05) = 0.0000

Calculate the square root of the right side: 0.0000

Break this problem into two subproblems by setting 
(y + 0.05) equal to 0.0000 and 0.0000.


Subproblem 1
y + 0.05 = 0.0000

Simplifying
y + 0.05 = 0.0000

Reorder the terms:
0.05 + y = 0.0000

Solving
0.05 + y = 0.0000

Solving for variable 'y'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + y = 0.0000 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + y = 0.0000 + -0.05
y = 0.0000 + -0.05

Combine like terms: 0.0000 + -0.05 = -0.05
y = -0.05

Simplifying
y = -0.05


Subproblem 2
y + 0.05 = 0.0000

Simplifying
y + 0.05 = 0.0000

Reorder the terms:
0.05 + y = 0.0000

Solving
0.05 + y = 0.0000

Solving for variable 'y'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + y = 0.0000 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + y = 0.0000 + -0.05
y = 0.0000 + -0.05

Combine like terms: 0.0000 + -0.05 = -0.05
y = -0.05

Simplifying
y = -0.05


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.05, -0.05}

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