21.16-9.2+1+y^2-4y+4=36

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Solution for 21.16-9.2+1+y^2-4y+4=36 equation: 


Simplifying
21.16 + -9.2 + 1 + y2 + -4y + 4 = 36

Reorder the terms:
21.16 + -9.2 + 1 + 4 + -4y + y2 = 36

Combine like terms: 21.16 + -9.2 = 11.96
11.96 + 1 + 4 + -4y + y2 = 36

Combine like terms: 11.96 + 1 = 12.96
12.96 + 4 + -4y + y2 = 36

Combine like terms: 12.96 + 4 = 16.96
16.96 + -4y + y2 = 36

Solving
16.96 + -4y + y2 = 36

Solving for variable 'y'.

Reorder the terms:
16.96 + -36 + -4y + y2 = 36 + -36

Combine like terms: 16.96 + -36 = -19.04
-19.04 + -4y + y2 = 36 + -36

Combine like terms: 36 + -36 = 0
-19.04 + -4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19.04' to each side of the equation.
-19.04 + -4y + 19.04 + y2 = 0 + 19.04

Reorder the terms:
-19.04 + 19.04 + -4y + y2 = 0 + 19.04

Combine like terms: -19.04 + 19.04 = 0.00
0.00 + -4y + y2 = 0 + 19.04
-4y + y2 = 0 + 19.04

Combine like terms: 0 + 19.04 = 19.04
-4y + y2 = 19.04

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 19.04 + 4

Reorder the terms:
4 + -4y + y2 = 19.04 + 4

Combine like terms: 19.04 + 4 = 23.04
4 + -4y + y2 = 23.04

Factor a perfect square on the left side:
(y + -2)(y + -2) = 23.04

Calculate the square root of the right side: 4.8

Break this problem into two subproblems by setting 
(y + -2) equal to 4.8 and -4.8.


Subproblem 1
y + -2 = 4.8

Simplifying
y + -2 = 4.8

Reorder the terms:
-2 + y = 4.8

Solving
-2 + y = 4.8

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 4.8 + 2

Combine like terms: -2 + 2 = 0
0 + y = 4.8 + 2
y = 4.8 + 2

Combine like terms: 4.8 + 2 = 6.8
y = 6.8

Simplifying
y = 6.8


Subproblem 2
y + -2 = -4.8

Simplifying
y + -2 = -4.8

Reorder the terms:
-2 + y = -4.8

Solving
-2 + y = -4.8

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -4.8 + 2

Combine like terms: -2 + 2 = 0
0 + y = -4.8 + 2
y = -4.8 + 2

Combine like terms: -4.8 + 2 = -2.8
y = -2.8

Simplifying
y = -2.8


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.8, -2.8}

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