y^2-6.4y+2.88=0

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Solution for y^2-6.4y+2.88=0 equation: 


Simplifying
y2 + -6.4y + 2.88 = 0

Reorder the terms:
2.88 + -6.4y + y2 = 0

Solving
2.88 + -6.4y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-2.88' to each side of the equation.
2.88 + -6.4y + -2.88 + y2 = 0 + -2.88

Reorder the terms:
2.88 + -2.88 + -6.4y + y2 = 0 + -2.88

Combine like terms: 2.88 + -2.88 = 0.00
0.00 + -6.4y + y2 = 0 + -2.88
-6.4y + y2 = 0 + -2.88

Combine like terms: 0 + -2.88 = -2.88
-6.4y + y2 = -2.88

The y term is -6.4y.  Take half its coefficient (-3.2).
Square it (10.24) and add it to both sides.

Add '10.24' to each side of the equation.
-6.4y + 10.24 + y2 = -2.88 + 10.24

Reorder the terms:
10.24 + -6.4y + y2 = -2.88 + 10.24

Combine like terms: -2.88 + 10.24 = 7.36
10.24 + -6.4y + y2 = 7.36

Factor a perfect square on the left side:
(y + -3.2)(y + -3.2) = 7.36

Calculate the square root of the right side: 2.712931993

Break this problem into two subproblems by setting 
(y + -3.2) equal to 2.712931993 and -2.712931993.


Subproblem 1
y + -3.2 = 2.712931993

Simplifying
y + -3.2 = 2.712931993

Reorder the terms:
-3.2 + y = 2.712931993

Solving
-3.2 + y = 2.712931993

Solving for variable 'y'.

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

Add '3.2' to each side of the equation.
-3.2 + 3.2 + y = 2.712931993 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + y = 2.712931993 + 3.2
y = 2.712931993 + 3.2

Combine like terms: 2.712931993 + 3.2 = 5.912931993
y = 5.912931993

Simplifying
y = 5.912931993


Subproblem 2
y + -3.2 = -2.712931993

Simplifying
y + -3.2 = -2.712931993

Reorder the terms:
-3.2 + y = -2.712931993

Solving
-3.2 + y = -2.712931993

Solving for variable 'y'.

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

Add '3.2' to each side of the equation.
-3.2 + 3.2 + y = -2.712931993 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + y = -2.712931993 + 3.2
y = -2.712931993 + 3.2

Combine like terms: -2.712931993 + 3.2 = 0.487068007
y = 0.487068007

Simplifying
y = 0.487068007


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.912931993, 0.487068007}

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