y^2-16y=272

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Solution for y^2-16y=272 equation:


Simplifying
y2 + -16y = 272

Reorder the terms:
-16y + y2 = 272

Solving
-16y + y2 = 272

Solving for variable 'y'.

Reorder the terms:
-272 + -16y + y2 = 272 + -272

Combine like terms: 272 + -272 = 0
-272 + -16y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '272' to each side of the equation.
-272 + -16y + 272 + y2 = 0 + 272

Reorder the terms:
-272 + 272 + -16y + y2 = 0 + 272

Combine like terms: -272 + 272 = 0
0 + -16y + y2 = 0 + 272
-16y + y2 = 0 + 272

Combine like terms: 0 + 272 = 272
-16y + y2 = 272

The y term is -16y.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16y + 64 + y2 = 272 + 64

Reorder the terms:
64 + -16y + y2 = 272 + 64

Combine like terms: 272 + 64 = 336
64 + -16y + y2 = 336

Factor a perfect square on the left side:
(y + -8)(y + -8) = 336

Calculate the square root of the right side: 18.33030278

Break this problem into two subproblems by setting 
(y + -8) equal to 18.33030278 and -18.33030278.

Subproblem 1

y + -8 = 18.33030278 Simplifying y + -8 = 18.33030278 Reorder the terms: -8 + y = 18.33030278 Solving -8 + y = 18.33030278 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = 18.33030278 + 8 Combine like terms: -8 + 8 = 0 0 + y = 18.33030278 + 8 y = 18.33030278 + 8 Combine like terms: 18.33030278 + 8 = 26.33030278 y = 26.33030278 Simplifying y = 26.33030278

Subproblem 2

y + -8 = -18.33030278 Simplifying y + -8 = -18.33030278 Reorder the terms: -8 + y = -18.33030278 Solving -8 + y = -18.33030278 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + y = -18.33030278 + 8 Combine like terms: -8 + 8 = 0 0 + y = -18.33030278 + 8 y = -18.33030278 + 8 Combine like terms: -18.33030278 + 8 = -10.33030278 y = -10.33030278 Simplifying y = -10.33030278

Solution

The solution to the problem is based on the solutions from the subproblems. y = {26.33030278, -10.33030278}

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