y^2-100y+500=0

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Solution for y^2-100y+500=0 equation: 


Simplifying
y2 + -100y + 500 = 0

Reorder the terms:
500 + -100y + y2 = 0

Solving
500 + -100y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-500' to each side of the equation.
500 + -100y + -500 + y2 = 0 + -500

Reorder the terms:
500 + -500 + -100y + y2 = 0 + -500

Combine like terms: 500 + -500 = 0
0 + -100y + y2 = 0 + -500
-100y + y2 = 0 + -500

Combine like terms: 0 + -500 = -500
-100y + y2 = -500

The y term is -100y.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100y + 2500 + y2 = -500 + 2500

Reorder the terms:
2500 + -100y + y2 = -500 + 2500

Combine like terms: -500 + 2500 = 2000
2500 + -100y + y2 = 2000

Factor a perfect square on the left side:
(y + -50)(y + -50) = 2000

Calculate the square root of the right side: 44.72135955

Break this problem into two subproblems by setting 
(y + -50) equal to 44.72135955 and -44.72135955.


Subproblem 1
y + -50 = 44.72135955

Simplifying
y + -50 = 44.72135955

Reorder the terms:
-50 + y = 44.72135955

Solving
-50 + y = 44.72135955

Solving for variable 'y'.

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

Add '50' to each side of the equation.
-50 + 50 + y = 44.72135955 + 50

Combine like terms: -50 + 50 = 0
0 + y = 44.72135955 + 50
y = 44.72135955 + 50

Combine like terms: 44.72135955 + 50 = 94.72135955
y = 94.72135955

Simplifying
y = 94.72135955


Subproblem 2
y + -50 = -44.72135955

Simplifying
y + -50 = -44.72135955

Reorder the terms:
-50 + y = -44.72135955

Solving
-50 + y = -44.72135955

Solving for variable 'y'.

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

Add '50' to each side of the equation.
-50 + 50 + y = -44.72135955 + 50

Combine like terms: -50 + 50 = 0
0 + y = -44.72135955 + 50
y = -44.72135955 + 50

Combine like terms: -44.72135955 + 50 = 5.27864045
y = 5.27864045

Simplifying
y = 5.27864045


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {94.72135955, 5.27864045}

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