y^2+0.25=y+4

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Solution for y^2+0.25=y+4 equation: 


Simplifying
y2 + 0.25 = y + 4

Reorder the terms:
0.25 + y2 = y + 4

Reorder the terms:
0.25 + y2 = 4 + y

Solving
0.25 + y2 = 4 + y

Solving for variable 'y'.

Reorder the terms:
0.25 + -4 + -1y + y2 = 4 + y + -4 + -1y

Combine like terms: 0.25 + -4 = -3.75
-3.75 + -1y + y2 = 4 + y + -4 + -1y

Reorder the terms:
-3.75 + -1y + y2 = 4 + -4 + y + -1y

Combine like terms: 4 + -4 = 0
-3.75 + -1y + y2 = 0 + y + -1y
-3.75 + -1y + y2 = y + -1y

Combine like terms: y + -1y = 0
-3.75 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -1y + 3.75 + y2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -1y + y2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -1y + y2 = 0 + 3.75
-1y + y2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-1y + y2 = 3.75

The y term is -1y.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1y + 0.25 + y2 = 3.75 + 0.25

Reorder the terms:
0.25 + -1y + y2 = 3.75 + 0.25

Combine like terms: 3.75 + 0.25 = 4
0.25 + -1y + y2 = 4

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting 
(y + -0.5) equal to 2 and -2.


Subproblem 1
y + -0.5 = 2

Simplifying
y + -0.5 = 2

Reorder the terms:
-0.5 + y = 2

Solving
-0.5 + y = 2

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = 2 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = 2 + 0.5
y = 2 + 0.5

Combine like terms: 2 + 0.5 = 2.5
y = 2.5

Simplifying
y = 2.5


Subproblem 2
y + -0.5 = -2

Simplifying
y + -0.5 = -2

Reorder the terms:
-0.5 + y = -2

Solving
-0.5 + y = -2

Solving for variable 'y'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + y = -2 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + y = -2 + 0.5
y = -2 + 0.5

Combine like terms: -2 + 0.5 = -1.5
y = -1.5

Simplifying
y = -1.5


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.5, -1.5}

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