y^2-19y+25=0

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Solution for y^2-19y+25=0 equation: 


Simplifying
y2 + -19y + 25 = 0

Reorder the terms:
25 + -19y + y2 = 0

Solving
25 + -19y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + -19y + -25 + y2 = 0 + -25

Reorder the terms:
25 + -25 + -19y + y2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -19y + y2 = 0 + -25
-19y + y2 = 0 + -25

Combine like terms: 0 + -25 = -25
-19y + y2 = -25

The y term is -19y.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19y + 90.25 + y2 = -25 + 90.25

Reorder the terms:
90.25 + -19y + y2 = -25 + 90.25

Combine like terms: -25 + 90.25 = 65.25
90.25 + -19y + y2 = 65.25

Factor a perfect square on the left side:
(y + -9.5)(y + -9.5) = 65.25

Calculate the square root of the right side: 8.077747211

Break this problem into two subproblems by setting 
(y + -9.5) equal to 8.077747211 and -8.077747211.


Subproblem 1
y + -9.5 = 8.077747211

Simplifying
y + -9.5 = 8.077747211

Reorder the terms:
-9.5 + y = 8.077747211

Solving
-9.5 + y = 8.077747211

Solving for variable 'y'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + y = 8.077747211 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + y = 8.077747211 + 9.5
y = 8.077747211 + 9.5

Combine like terms: 8.077747211 + 9.5 = 17.577747211
y = 17.577747211

Simplifying
y = 17.577747211


Subproblem 2
y + -9.5 = -8.077747211

Simplifying
y + -9.5 = -8.077747211

Reorder the terms:
-9.5 + y = -8.077747211

Solving
-9.5 + y = -8.077747211

Solving for variable 'y'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + y = -8.077747211 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + y = -8.077747211 + 9.5
y = -8.077747211 + 9.5

Combine like terms: -8.077747211 + 9.5 = 1.422252789
y = 1.422252789

Simplifying
y = 1.422252789


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {17.577747211, 1.422252789}

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