4.76-y=y^2

Solution for 4.76-y=y^2 equation:

Simplifying
4.76 + -1y = y2

Solving
4.76 + -1y = y2

Solving for variable 'y'.

Combine like terms: y2 + -1y2 = 0
4.76 + -1y + -1y2 = 0

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

Divide each side by '-1'.
-4.76 + y + y2 = 0

Move the constant term to the right:

Add '4.76' to each side of the equation.
-4.76 + y + 4.76 + y2 = 0 + 4.76

Reorder the terms:
-4.76 + 4.76 + y + y2 = 0 + 4.76

Combine like terms: -4.76 + 4.76 = 0.00
0.00 + y + y2 = 0 + 4.76
y + y2 = 0 + 4.76

Combine like terms: 0 + 4.76 = 4.76
y + y2 = 4.76

The y term is y.  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.
 + 0.25 + y2 = 4.76 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + y2 = 4.76 + 0.25

Combine like terms: 4.76 + 0.25 = 5.01
1.25 + y2 = 5.01

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 5.01

Calculate the square root of the right side: 2.238302929

Break this problem into two subproblems by setting 
(y + 0.5) equal to 2.238302929 and -2.238302929.

Subproblem 1
y + 0.5 = 2.238302929

Simplifying
y + 0.5 = 2.238302929

Reorder the terms:
0.5 + y = 2.238302929

Solving
0.5 + y = 2.238302929

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 = 2.238302929 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 2.238302929 + -0.5
y = 2.238302929 + -0.5

Combine like terms: 2.238302929 + -0.5 = 1.738302929
y = 1.738302929

Simplifying
y = 1.738302929

Subproblem 2
y + 0.5 = -2.238302929

Simplifying
y + 0.5 = -2.238302929

Reorder the terms:
0.5 + y = -2.238302929

Solving
0.5 + y = -2.238302929

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 = -2.238302929 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -2.238302929 + -0.5
y = -2.238302929 + -0.5

Combine like terms: -2.238302929 + -0.5 = -2.738302929
y = -2.738302929

Simplifying
y = -2.738302929

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.738302929, -2.738302929}