(y*2-50)*(y*2-50)=2

Solution for (y*2-50)*(y*2-50)=2 equation:

Simplifying
(y * 2 + -50)(y * 2 + -50) = 2

Reorder the terms for easier multiplication:
(2y + -50)(y * 2 + -50) = 2

Reorder the terms:
(-50 + 2y)(y * 2 + -50) = 2

Reorder the terms for easier multiplication:
(-50 + 2y)(2y + -50) = 2

Reorder the terms:
(-50 + 2y)(-50 + 2y) = 2

Multiply (-50 + 2y) * (-50 + 2y)
(-50(-50 + 2y) + 2y * (-50 + 2y)) = 2
((-50 * -50 + 2y * -50) + 2y * (-50 + 2y)) = 2
((2500 + -100y) + 2y * (-50 + 2y)) = 2
(2500 + -100y + (-50 * 2y + 2y * 2y)) = 2
(2500 + -100y + (-100y + 4y2)) = 2

Combine like terms: -100y + -100y = -200y
(2500 + -200y + 4y2) = 2

Solving
2500 + -200y + 4y2 = 2

Solving for variable 'y'.

Reorder the terms:
2500 + -2 + -200y + 4y2 = 2 + -2

Combine like terms: 2500 + -2 = 2498
2498 + -200y + 4y2 = 2 + -2

Combine like terms: 2 + -2 = 0
2498 + -200y + 4y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1249 + -100y + 2y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1249 + -100y + 2y2)' equal to zero and attempt to solve:

Simplifying
1249 + -100y + 2y2 = 0

Solving
1249 + -100y + 2y2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
624.5 + -50y + y2 = 0

Move the constant term to the right:

Add '-624.5' to each side of the equation.
624.5 + -50y + -624.5 + y2 = 0 + -624.5

Reorder the terms:
624.5 + -624.5 + -50y + y2 = 0 + -624.5

Combine like terms: 624.5 + -624.5 = 0.0
0.0 + -50y + y2 = 0 + -624.5
-50y + y2 = 0 + -624.5

Combine like terms: 0 + -624.5 = -624.5
-50y + y2 = -624.5

The y term is -50y.  Take half its coefficient (-25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
-50y + 625 + y2 = -624.5 + 625

Reorder the terms:
625 + -50y + y2 = -624.5 + 625

Combine like terms: -624.5 + 625 = 0.5
625 + -50y + y2 = 0.5

Factor a perfect square on the left side:
(y + -25)(y + -25) = 0.5

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(y + -25) equal to 0.707106781 and -0.707106781.

Subproblem 1
y + -25 = 0.707106781

Simplifying
y + -25 = 0.707106781

Reorder the terms:
-25 + y = 0.707106781

Solving
-25 + y = 0.707106781

Solving for variable 'y'.

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

Add '25' to each side of the equation.
-25 + 25 + y = 0.707106781 + 25

Combine like terms: -25 + 25 = 0
0 + y = 0.707106781 + 25
y = 0.707106781 + 25

Combine like terms: 0.707106781 + 25 = 25.707106781
y = 25.707106781

Simplifying
y = 25.707106781

Subproblem 2
y + -25 = -0.707106781

Simplifying
y + -25 = -0.707106781

Reorder the terms:
-25 + y = -0.707106781

Solving
-25 + y = -0.707106781

Solving for variable 'y'.

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

Add '25' to each side of the equation.
-25 + 25 + y = -0.707106781 + 25

Combine like terms: -25 + 25 = 0
0 + y = -0.707106781 + 25
y = -0.707106781 + 25

Combine like terms: -0.707106781 + 25 = 24.292893219
y = 24.292893219

Simplifying
y = 24.292893219

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {25.707106781, 24.292893219}
Solution
y = {25.707106781, 24.292893219}