(y^2)-18y+35=0

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Solution for (y^2)-18y+35=0 equation: 


Simplifying
(y2) + -18y + 35 = 0
y2 + -18y + 35 = 0

Reorder the terms:
35 + -18y + y2 = 0

Solving
35 + -18y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -18y + -35 + y2 = 0 + -35

Reorder the terms:
35 + -35 + -18y + y2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -18y + y2 = 0 + -35
-18y + y2 = 0 + -35

Combine like terms: 0 + -35 = -35
-18y + y2 = -35

The y term is -18y.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18y + 81 + y2 = -35 + 81

Reorder the terms:
81 + -18y + y2 = -35 + 81

Combine like terms: -35 + 81 = 46
81 + -18y + y2 = 46

Factor a perfect square on the left side:
(y + -9)(y + -9) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(y + -9) equal to 6.782329983 and -6.782329983.


Subproblem 1
y + -9 = 6.782329983

Simplifying
y + -9 = 6.782329983

Reorder the terms:
-9 + y = 6.782329983

Solving
-9 + y = 6.782329983

Solving for variable 'y'.

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

Add '9' to each side of the equation.
-9 + 9 + y = 6.782329983 + 9

Combine like terms: -9 + 9 = 0
0 + y = 6.782329983 + 9
y = 6.782329983 + 9

Combine like terms: 6.782329983 + 9 = 15.782329983
y = 15.782329983

Simplifying
y = 15.782329983


Subproblem 2
y + -9 = -6.782329983

Simplifying
y + -9 = -6.782329983

Reorder the terms:
-9 + y = -6.782329983

Solving
-9 + y = -6.782329983

Solving for variable 'y'.

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

Add '9' to each side of the equation.
-9 + 9 + y = -6.782329983 + 9

Combine like terms: -9 + 9 = 0
0 + y = -6.782329983 + 9
y = -6.782329983 + 9

Combine like terms: -6.782329983 + 9 = 2.217670017
y = 2.217670017

Simplifying
y = 2.217670017


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {15.782329983, 2.217670017}

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