y[y-19]=-64

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Solution for y[y-19]=-64 equation: 


Simplifying
y[y + -19] = -64

Reorder the terms:
y[-19 + y] = -64
[-19 * y + y * y] = -64
[-19y + y2] = -64

Solving
-19y + y2 = -64

Solving for variable 'y'.

Reorder the terms:
64 + -19y + y2 = -64 + 64

Combine like terms: -64 + 64 = 0
64 + -19y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -19y + -64 + y2 = 0 + -64

Reorder the terms:
64 + -64 + -19y + y2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -19y + y2 = 0 + -64
-19y + y2 = 0 + -64

Combine like terms: 0 + -64 = -64
-19y + y2 = -64

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 = -64 + 90.25

Reorder the terms:
90.25 + -19y + y2 = -64 + 90.25

Combine like terms: -64 + 90.25 = 26.25
90.25 + -19y + y2 = 26.25

Factor a perfect square on the left side:
(y + -9.5)(y + -9.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(y + -9.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
y + -9.5 = 5.123475383

Simplifying
y + -9.5 = 5.123475383

Reorder the terms:
-9.5 + y = 5.123475383

Solving
-9.5 + y = 5.123475383

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 = 5.123475383 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + y = 5.123475383 + 9.5
y = 5.123475383 + 9.5

Combine like terms: 5.123475383 + 9.5 = 14.623475383
y = 14.623475383

Simplifying
y = 14.623475383


Subproblem 2
y + -9.5 = -5.123475383

Simplifying
y + -9.5 = -5.123475383

Reorder the terms:
-9.5 + y = -5.123475383

Solving
-9.5 + y = -5.123475383

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 = -5.123475383 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + y = -5.123475383 + 9.5
y = -5.123475383 + 9.5

Combine like terms: -5.123475383 + 9.5 = 4.376524617
y = 4.376524617

Simplifying
y = 4.376524617


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {14.623475383, 4.376524617}

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