(y-6)(y-6)-50=0

Solution for (y-6)(y-6)-50=0 equation:

Simplifying
(y + -6)(y + -6) + -50 = 0

Reorder the terms:
(-6 + y)(y + -6) + -50 = 0

Reorder the terms:
(-6 + y)(-6 + y) + -50 = 0

Multiply (-6 + y) * (-6 + y)
(-6(-6 + y) + y(-6 + y)) + -50 = 0
((-6 * -6 + y * -6) + y(-6 + y)) + -50 = 0
((36 + -6y) + y(-6 + y)) + -50 = 0
(36 + -6y + (-6 * y + y * y)) + -50 = 0
(36 + -6y + (-6y + y2)) + -50 = 0

Combine like terms: -6y + -6y = -12y
(36 + -12y + y2) + -50 = 0

Reorder the terms:
36 + -50 + -12y + y2 = 0

Combine like terms: 36 + -50 = -14
-14 + -12y + y2 = 0

Solving
-14 + -12y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -12y + 14 + y2 = 0 + 14

Reorder the terms:
-14 + 14 + -12y + y2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -12y + y2 = 0 + 14
-12y + y2 = 0 + 14

Combine like terms: 0 + 14 = 14
-12y + y2 = 14

The y term is -12y.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12y + 36 + y2 = 14 + 36

Reorder the terms:
36 + -12y + y2 = 14 + 36

Combine like terms: 14 + 36 = 50
36 + -12y + y2 = 50

Factor a perfect square on the left side:
(y + -6)(y + -6) = 50

Calculate the square root of the right side: 7.071067812

Break this problem into two subproblems by setting 
(y + -6) equal to 7.071067812 and -7.071067812.

Subproblem 1
y + -6 = 7.071067812

Simplifying
y + -6 = 7.071067812

Reorder the terms:
-6 + y = 7.071067812

Solving
-6 + y = 7.071067812

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = 7.071067812 + 6

Combine like terms: -6 + 6 = 0
0 + y = 7.071067812 + 6
y = 7.071067812 + 6

Combine like terms: 7.071067812 + 6 = 13.071067812
y = 13.071067812

Simplifying
y = 13.071067812

Subproblem 2
y + -6 = -7.071067812

Simplifying
y + -6 = -7.071067812

Reorder the terms:
-6 + y = -7.071067812

Solving
-6 + y = -7.071067812

Solving for variable 'y'.

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

Add '6' to each side of the equation.
-6 + 6 + y = -7.071067812 + 6

Combine like terms: -6 + 6 = 0
0 + y = -7.071067812 + 6
y = -7.071067812 + 6

Combine like terms: -7.071067812 + 6 = -1.071067812
y = -1.071067812

Simplifying
y = -1.071067812

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {13.071067812, -1.071067812}