y(y-4)=44

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Solution for y(y-4)=44 equation:


Simplifying
y(y + -4) = 44

Reorder the terms:
y(-4 + y) = 44
(-4 * y + y * y) = 44
(-4y + y2) = 44

Solving
-4y + y2 = 44

Solving for variable 'y'.

Reorder the terms:
-44 + -4y + y2 = 44 + -44

Combine like terms: 44 + -44 = 0
-44 + -4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '44' to each side of the equation.
-44 + -4y + 44 + y2 = 0 + 44

Reorder the terms:
-44 + 44 + -4y + y2 = 0 + 44

Combine like terms: -44 + 44 = 0
0 + -4y + y2 = 0 + 44
-4y + y2 = 0 + 44

Combine like terms: 0 + 44 = 44
-4y + y2 = 44

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 44 + 4

Reorder the terms:
4 + -4y + y2 = 44 + 4

Combine like terms: 44 + 4 = 48
4 + -4y + y2 = 48

Factor a perfect square on the left side:
(y + -2)(y + -2) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(y + -2) equal to 6.92820323 and -6.92820323.

Subproblem 1

y + -2 = 6.92820323 Simplifying y + -2 = 6.92820323 Reorder the terms: -2 + y = 6.92820323 Solving -2 + y = 6.92820323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 6.92820323 + 2 Combine like terms: -2 + 2 = 0 0 + y = 6.92820323 + 2 y = 6.92820323 + 2 Combine like terms: 6.92820323 + 2 = 8.92820323 y = 8.92820323 Simplifying y = 8.92820323

Subproblem 2

y + -2 = -6.92820323 Simplifying y + -2 = -6.92820323 Reorder the terms: -2 + y = -6.92820323 Solving -2 + y = -6.92820323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -6.92820323 + 2 Combine like terms: -2 + 2 = 0 0 + y = -6.92820323 + 2 y = -6.92820323 + 2 Combine like terms: -6.92820323 + 2 = -4.92820323 y = -4.92820323 Simplifying y = -4.92820323

Solution

The solution to the problem is based on the solutions from the subproblems. y = {8.92820323, -4.92820323}

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