y^2-80y+600=0

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Solution for y^2-80y+600=0 equation: 


Simplifying
y2 + -80y + 600 = 0

Reorder the terms:
600 + -80y + y2 = 0

Solving
600 + -80y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + -80y + -600 + y2 = 0 + -600

Reorder the terms:
600 + -600 + -80y + y2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + -80y + y2 = 0 + -600
-80y + y2 = 0 + -600

Combine like terms: 0 + -600 = -600
-80y + y2 = -600

The y term is -80y.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80y + 1600 + y2 = -600 + 1600

Reorder the terms:
1600 + -80y + y2 = -600 + 1600

Combine like terms: -600 + 1600 = 1000
1600 + -80y + y2 = 1000

Factor a perfect square on the left side:
(y + -40)(y + -40) = 1000

Calculate the square root of the right side: 31.622776602

Break this problem into two subproblems by setting 
(y + -40) equal to 31.622776602 and -31.622776602.


Subproblem 1
y + -40 = 31.622776602

Simplifying
y + -40 = 31.622776602

Reorder the terms:
-40 + y = 31.622776602

Solving
-40 + y = 31.622776602

Solving for variable 'y'.

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

Add '40' to each side of the equation.
-40 + 40 + y = 31.622776602 + 40

Combine like terms: -40 + 40 = 0
0 + y = 31.622776602 + 40
y = 31.622776602 + 40

Combine like terms: 31.622776602 + 40 = 71.622776602
y = 71.622776602

Simplifying
y = 71.622776602


Subproblem 2
y + -40 = -31.622776602

Simplifying
y + -40 = -31.622776602

Reorder the terms:
-40 + y = -31.622776602

Solving
-40 + y = -31.622776602

Solving for variable 'y'.

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

Add '40' to each side of the equation.
-40 + 40 + y = -31.622776602 + 40

Combine like terms: -40 + 40 = 0
0 + y = -31.622776602 + 40
y = -31.622776602 + 40

Combine like terms: -31.622776602 + 40 = 8.377223398
y = 8.377223398

Simplifying
y = 8.377223398


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {71.622776602, 8.377223398}

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