y^2-40y+200=0

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Solution for y^2-40y+200=0 equation: 


Simplifying
y2 + -40y + 200 = 0

Reorder the terms:
200 + -40y + y2 = 0

Solving
200 + -40y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-200' to each side of the equation.
200 + -40y + -200 + y2 = 0 + -200

Reorder the terms:
200 + -200 + -40y + y2 = 0 + -200

Combine like terms: 200 + -200 = 0
0 + -40y + y2 = 0 + -200
-40y + y2 = 0 + -200

Combine like terms: 0 + -200 = -200
-40y + y2 = -200

The y term is -40y.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40y + 400 + y2 = -200 + 400

Reorder the terms:
400 + -40y + y2 = -200 + 400

Combine like terms: -200 + 400 = 200
400 + -40y + y2 = 200

Factor a perfect square on the left side:
(y + -20)(y + -20) = 200

Calculate the square root of the right side: 14.142135624

Break this problem into two subproblems by setting 
(y + -20) equal to 14.142135624 and -14.142135624.


Subproblem 1
y + -20 = 14.142135624

Simplifying
y + -20 = 14.142135624

Reorder the terms:
-20 + y = 14.142135624

Solving
-20 + y = 14.142135624

Solving for variable 'y'.

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

Add '20' to each side of the equation.
-20 + 20 + y = 14.142135624 + 20

Combine like terms: -20 + 20 = 0
0 + y = 14.142135624 + 20
y = 14.142135624 + 20

Combine like terms: 14.142135624 + 20 = 34.142135624
y = 34.142135624

Simplifying
y = 34.142135624


Subproblem 2
y + -20 = -14.142135624

Simplifying
y + -20 = -14.142135624

Reorder the terms:
-20 + y = -14.142135624

Solving
-20 + y = -14.142135624

Solving for variable 'y'.

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

Add '20' to each side of the equation.
-20 + 20 + y = -14.142135624 + 20

Combine like terms: -20 + 20 = 0
0 + y = -14.142135624 + 20
y = -14.142135624 + 20

Combine like terms: -14.142135624 + 20 = 5.857864376
y = 5.857864376

Simplifying
y = 5.857864376


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {34.142135624, 5.857864376}

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