0.5y+0.1=y^2

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Solution for 0.5y+0.1=y^2 equation: 


Simplifying
0.5y + 0.1 = y2

Reorder the terms:
0.1 + 0.5y = y2

Solving
0.1 + 0.5y = y2

Solving for variable 'y'.

Combine like terms: y2 + -1y2 = 0
0.1 + 0.5y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-0.1 + -0.5y + y2 = 0

Move the constant term to the right:

Add '0.1' to each side of the equation.
-0.1 + -0.5y + 0.1 + y2 = 0 + 0.1

Reorder the terms:
-0.1 + 0.1 + -0.5y + y2 = 0 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + -0.5y + y2 = 0 + 0.1
-0.5y + y2 = 0 + 0.1

Combine like terms: 0 + 0.1 = 0.1
-0.5y + y2 = 0.1

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 = 0.1 + 0.0625

Reorder the terms:
0.0625 + -0.5y + y2 = 0.1 + 0.0625

Combine like terms: 0.1 + 0.0625 = 0.1625
0.0625 + -0.5y + y2 = 0.1625

Factor a perfect square on the left side:
(y + -0.25)(y + -0.25) = 0.1625

Calculate the square root of the right side: 0.403112887

Break this problem into two subproblems by setting 
(y + -0.25) equal to 0.403112887 and -0.403112887.


Subproblem 1
y + -0.25 = 0.403112887

Simplifying
y + -0.25 = 0.403112887

Reorder the terms:
-0.25 + y = 0.403112887

Solving
-0.25 + y = 0.403112887

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 = 0.403112887 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = 0.403112887 + 0.25
y = 0.403112887 + 0.25

Combine like terms: 0.403112887 + 0.25 = 0.653112887
y = 0.653112887

Simplifying
y = 0.653112887


Subproblem 2
y + -0.25 = -0.403112887

Simplifying
y + -0.25 = -0.403112887

Reorder the terms:
-0.25 + y = -0.403112887

Solving
-0.25 + y = -0.403112887

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 = -0.403112887 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + y = -0.403112887 + 0.25
y = -0.403112887 + 0.25

Combine like terms: -0.403112887 + 0.25 = -0.153112887
y = -0.153112887

Simplifying
y = -0.153112887


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.653112887, -0.153112887}

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