y^2-64y+256=0

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Solution for y^2-64y+256=0 equation:


Simplifying
y2 + -64y + 256 = 0

Reorder the terms:
256 + -64y + y2 = 0

Solving
256 + -64y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-256' to each side of the equation.
256 + -64y + -256 + y2 = 0 + -256

Reorder the terms:
256 + -256 + -64y + y2 = 0 + -256

Combine like terms: 256 + -256 = 0
0 + -64y + y2 = 0 + -256
-64y + y2 = 0 + -256

Combine like terms: 0 + -256 = -256
-64y + y2 = -256

The y term is -64y.  Take half its coefficient (-32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
-64y + 1024 + y2 = -256 + 1024

Reorder the terms:
1024 + -64y + y2 = -256 + 1024

Combine like terms: -256 + 1024 = 768
1024 + -64y + y2 = 768

Factor a perfect square on the left side:
(y + -32)(y + -32) = 768

Calculate the square root of the right side: 27.712812921

Break this problem into two subproblems by setting 
(y + -32) equal to 27.712812921 and -27.712812921.

Subproblem 1

y + -32 = 27.712812921 Simplifying y + -32 = 27.712812921 Reorder the terms: -32 + y = 27.712812921 Solving -32 + y = 27.712812921 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + y = 27.712812921 + 32 Combine like terms: -32 + 32 = 0 0 + y = 27.712812921 + 32 y = 27.712812921 + 32 Combine like terms: 27.712812921 + 32 = 59.712812921 y = 59.712812921 Simplifying y = 59.712812921

Subproblem 2

y + -32 = -27.712812921 Simplifying y + -32 = -27.712812921 Reorder the terms: -32 + y = -27.712812921 Solving -32 + y = -27.712812921 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + y = -27.712812921 + 32 Combine like terms: -32 + 32 = 0 0 + y = -27.712812921 + 32 y = -27.712812921 + 32 Combine like terms: -27.712812921 + 32 = 4.287187079 y = 4.287187079 Simplifying y = 4.287187079

Solution

The solution to the problem is based on the solutions from the subproblems. y = {59.712812921, 4.287187079}

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