y^2+0.5y+0.0625=0

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Solution for y^2+0.5y+0.0625=0 equation: 


Simplifying
y2 + 0.5y + 0.0625 = 0

Reorder the terms:
0.0625 + 0.5y + y2 = 0

Solving
0.0625 + 0.5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-0.0625' to each side of the equation.
0.0625 + 0.5y + -0.0625 + y2 = 0 + -0.0625

Reorder the terms:
0.0625 + -0.0625 + 0.5y + y2 = 0 + -0.0625

Combine like terms: 0.0625 + -0.0625 = 0.0000
0.0000 + 0.5y + y2 = 0 + -0.0625
0.5y + y2 = 0 + -0.0625

Combine like terms: 0 + -0.0625 = -0.0625
0.5y + y2 = -0.0625

The y term is 0.5y.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5y + 0.0625 + y2 = -0.0625 + 0.0625

Reorder the terms:
0.0625 + 0.5y + y2 = -0.0625 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0625 + 0.5y + y2 = 0.0000

Factor a perfect square on the left side:
(y + 0.25)(y + 0.25) = 0.0000

Calculate the square root of the right side: 0.0000

Break this problem into two subproblems by setting 
(y + 0.25) equal to 0.0000 and 0.0000.


Subproblem 1
y + 0.25 = 0.0000

Simplifying
y + 0.25 = 0.0000

Reorder the terms:
0.25 + y = 0.0000

Solving
0.25 + y = 0.0000

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = 0.0000 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = 0.0000 + -0.25
y = 0.0000 + -0.25

Combine like terms: 0.0000 + -0.25 = -0.25
y = -0.25

Simplifying
y = -0.25


Subproblem 2
y + 0.25 = 0.0000

Simplifying
y + 0.25 = 0.0000

Reorder the terms:
0.25 + y = 0.0000

Solving
0.25 + y = 0.0000

Solving for variable 'y'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + y = 0.0000 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + y = 0.0000 + -0.25
y = 0.0000 + -0.25

Combine like terms: 0.0000 + -0.25 = -0.25
y = -0.25

Simplifying
y = -0.25


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.25, -0.25}

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