y^2-30y+185=0

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Solution for y^2-30y+185=0 equation: 


Simplifying
y2 + -30y + 185 = 0

Reorder the terms:
185 + -30y + y2 = 0

Solving
185 + -30y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-185' to each side of the equation.
185 + -30y + -185 + y2 = 0 + -185

Reorder the terms:
185 + -185 + -30y + y2 = 0 + -185

Combine like terms: 185 + -185 = 0
0 + -30y + y2 = 0 + -185
-30y + y2 = 0 + -185

Combine like terms: 0 + -185 = -185
-30y + y2 = -185

The y term is -30y.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30y + 225 + y2 = -185 + 225

Reorder the terms:
225 + -30y + y2 = -185 + 225

Combine like terms: -185 + 225 = 40
225 + -30y + y2 = 40

Factor a perfect square on the left side:
(y + -15)(y + -15) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(y + -15) equal to 6.32455532 and -6.32455532.


Subproblem 1
y + -15 = 6.32455532

Simplifying
y + -15 = 6.32455532

Reorder the terms:
-15 + y = 6.32455532

Solving
-15 + y = 6.32455532

Solving for variable 'y'.

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

Add '15' to each side of the equation.
-15 + 15 + y = 6.32455532 + 15

Combine like terms: -15 + 15 = 0
0 + y = 6.32455532 + 15
y = 6.32455532 + 15

Combine like terms: 6.32455532 + 15 = 21.32455532
y = 21.32455532

Simplifying
y = 21.32455532


Subproblem 2
y + -15 = -6.32455532

Simplifying
y + -15 = -6.32455532

Reorder the terms:
-15 + y = -6.32455532

Solving
-15 + y = -6.32455532

Solving for variable 'y'.

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

Add '15' to each side of the equation.
-15 + 15 + y = -6.32455532 + 15

Combine like terms: -15 + 15 = 0
0 + y = -6.32455532 + 15
y = -6.32455532 + 15

Combine like terms: -6.32455532 + 15 = 8.67544468
y = 8.67544468

Simplifying
y = 8.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {21.32455532, 8.67544468}

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