y^2-60y+175=0

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Solution for y^2-60y+175=0 equation: 


Simplifying
y2 + -60y + 175 = 0

Reorder the terms:
175 + -60y + y2 = 0

Solving
175 + -60y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-175' to each side of the equation.
175 + -60y + -175 + y2 = 0 + -175

Reorder the terms:
175 + -175 + -60y + y2 = 0 + -175

Combine like terms: 175 + -175 = 0
0 + -60y + y2 = 0 + -175
-60y + y2 = 0 + -175

Combine like terms: 0 + -175 = -175
-60y + y2 = -175

The y term is -60y.  Take half its coefficient (-30).
Square it (900) and add it to both sides.

Add '900' to each side of the equation.
-60y + 900 + y2 = -175 + 900

Reorder the terms:
900 + -60y + y2 = -175 + 900

Combine like terms: -175 + 900 = 725
900 + -60y + y2 = 725

Factor a perfect square on the left side:
(y + -30)(y + -30) = 725

Calculate the square root of the right side: 26.925824036

Break this problem into two subproblems by setting 
(y + -30) equal to 26.925824036 and -26.925824036.


Subproblem 1
y + -30 = 26.925824036

Simplifying
y + -30 = 26.925824036

Reorder the terms:
-30 + y = 26.925824036

Solving
-30 + y = 26.925824036

Solving for variable 'y'.

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

Add '30' to each side of the equation.
-30 + 30 + y = 26.925824036 + 30

Combine like terms: -30 + 30 = 0
0 + y = 26.925824036 + 30
y = 26.925824036 + 30

Combine like terms: 26.925824036 + 30 = 56.925824036
y = 56.925824036

Simplifying
y = 56.925824036


Subproblem 2
y + -30 = -26.925824036

Simplifying
y + -30 = -26.925824036

Reorder the terms:
-30 + y = -26.925824036

Solving
-30 + y = -26.925824036

Solving for variable 'y'.

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

Add '30' to each side of the equation.
-30 + 30 + y = -26.925824036 + 30

Combine like terms: -30 + 30 = 0
0 + y = -26.925824036 + 30
y = -26.925824036 + 30

Combine like terms: -26.925824036 + 30 = 3.074175964
y = 3.074175964

Simplifying
y = 3.074175964


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {56.925824036, 3.074175964}

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