(y^2)-18y+30=0

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Solution for (y^2)-18y+30=0 equation: 


Simplifying
(y2) + -18y + 30 = 0
y2 + -18y + 30 = 0

Reorder the terms:
30 + -18y + y2 = 0

Solving
30 + -18y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + -18y + -30 + y2 = 0 + -30

Reorder the terms:
30 + -30 + -18y + y2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + -18y + y2 = 0 + -30
-18y + y2 = 0 + -30

Combine like terms: 0 + -30 = -30
-18y + y2 = -30

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 = -30 + 81

Reorder the terms:
81 + -18y + y2 = -30 + 81

Combine like terms: -30 + 81 = 51
81 + -18y + y2 = 51

Factor a perfect square on the left side:
(y + -9)(y + -9) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(y + -9) equal to 7.141428429 and -7.141428429.


Subproblem 1
y + -9 = 7.141428429

Simplifying
y + -9 = 7.141428429

Reorder the terms:
-9 + y = 7.141428429

Solving
-9 + y = 7.141428429

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 = 7.141428429 + 9

Combine like terms: -9 + 9 = 0
0 + y = 7.141428429 + 9
y = 7.141428429 + 9

Combine like terms: 7.141428429 + 9 = 16.141428429
y = 16.141428429

Simplifying
y = 16.141428429


Subproblem 2
y + -9 = -7.141428429

Simplifying
y + -9 = -7.141428429

Reorder the terms:
-9 + y = -7.141428429

Solving
-9 + y = -7.141428429

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 = -7.141428429 + 9

Combine like terms: -9 + 9 = 0
0 + y = -7.141428429 + 9
y = -7.141428429 + 9

Combine like terms: -7.141428429 + 9 = 1.858571571
y = 1.858571571

Simplifying
y = 1.858571571


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {16.141428429, 1.858571571}

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