y^2-36y-64=0

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Solution for y^2-36y-64=0 equation: 


Simplifying
y2 + -36y + -64 = 0

Reorder the terms:
-64 + -36y + y2 = 0

Solving
-64 + -36y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + -36y + 64 + y2 = 0 + 64

Reorder the terms:
-64 + 64 + -36y + y2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + -36y + y2 = 0 + 64
-36y + y2 = 0 + 64

Combine like terms: 0 + 64 = 64
-36y + y2 = 64

The y term is -36y.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36y + 324 + y2 = 64 + 324

Reorder the terms:
324 + -36y + y2 = 64 + 324

Combine like terms: 64 + 324 = 388
324 + -36y + y2 = 388

Factor a perfect square on the left side:
(y + -18)(y + -18) = 388

Calculate the square root of the right side: 19.697715604

Break this problem into two subproblems by setting 
(y + -18) equal to 19.697715604 and -19.697715604.


Subproblem 1
y + -18 = 19.697715604

Simplifying
y + -18 = 19.697715604

Reorder the terms:
-18 + y = 19.697715604

Solving
-18 + y = 19.697715604

Solving for variable 'y'.

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

Add '18' to each side of the equation.
-18 + 18 + y = 19.697715604 + 18

Combine like terms: -18 + 18 = 0
0 + y = 19.697715604 + 18
y = 19.697715604 + 18

Combine like terms: 19.697715604 + 18 = 37.697715604
y = 37.697715604

Simplifying
y = 37.697715604


Subproblem 2
y + -18 = -19.697715604

Simplifying
y + -18 = -19.697715604

Reorder the terms:
-18 + y = -19.697715604

Solving
-18 + y = -19.697715604

Solving for variable 'y'.

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

Add '18' to each side of the equation.
-18 + 18 + y = -19.697715604 + 18

Combine like terms: -18 + 18 = 0
0 + y = -19.697715604 + 18
y = -19.697715604 + 18

Combine like terms: -19.697715604 + 18 = -1.697715604
y = -1.697715604

Simplifying
y = -1.697715604


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {37.697715604, -1.697715604}

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