y^2-125y-444=0

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Solution for y^2-125y-444=0 equation: 


Simplifying
y2 + -125y + -444 = 0

Reorder the terms:
-444 + -125y + y2 = 0

Solving
-444 + -125y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '444' to each side of the equation.
-444 + -125y + 444 + y2 = 0 + 444

Reorder the terms:
-444 + 444 + -125y + y2 = 0 + 444

Combine like terms: -444 + 444 = 0
0 + -125y + y2 = 0 + 444
-125y + y2 = 0 + 444

Combine like terms: 0 + 444 = 444
-125y + y2 = 444

The y term is -125y.  Take half its coefficient (-62.5).
Square it (3906.25) and add it to both sides.

Add '3906.25' to each side of the equation.
-125y + 3906.25 + y2 = 444 + 3906.25

Reorder the terms:
3906.25 + -125y + y2 = 444 + 3906.25

Combine like terms: 444 + 3906.25 = 4350.25
3906.25 + -125y + y2 = 4350.25

Factor a perfect square on the left side:
(y + -62.5)(y + -62.5) = 4350.25

Calculate the square root of the right side: 65.956425009

Break this problem into two subproblems by setting 
(y + -62.5) equal to 65.956425009 and -65.956425009.


Subproblem 1
y + -62.5 = 65.956425009

Simplifying
y + -62.5 = 65.956425009

Reorder the terms:
-62.5 + y = 65.956425009

Solving
-62.5 + y = 65.956425009

Solving for variable 'y'.

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

Add '62.5' to each side of the equation.
-62.5 + 62.5 + y = 65.956425009 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + y = 65.956425009 + 62.5
y = 65.956425009 + 62.5

Combine like terms: 65.956425009 + 62.5 = 128.456425009
y = 128.456425009

Simplifying
y = 128.456425009


Subproblem 2
y + -62.5 = -65.956425009

Simplifying
y + -62.5 = -65.956425009

Reorder the terms:
-62.5 + y = -65.956425009

Solving
-62.5 + y = -65.956425009

Solving for variable 'y'.

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

Add '62.5' to each side of the equation.
-62.5 + 62.5 + y = -65.956425009 + 62.5

Combine like terms: -62.5 + 62.5 = 0.0
0.0 + y = -65.956425009 + 62.5
y = -65.956425009 + 62.5

Combine like terms: -65.956425009 + 62.5 = -3.456425009
y = -3.456425009

Simplifying
y = -3.456425009


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {128.456425009, -3.456425009}

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