y^2-4y-16=0

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Solution for y^2-4y-16=0 equation: 


Simplifying
y2 + -4y + -16 = 0

Reorder the terms:
-16 + -4y + y2 = 0

Solving
-16 + -4y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -4y + 16 + y2 = 0 + 16

Reorder the terms:
-16 + 16 + -4y + y2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -4y + y2 = 0 + 16
-4y + y2 = 0 + 16

Combine like terms: 0 + 16 = 16
-4y + y2 = 16

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 = 16 + 4

Reorder the terms:
4 + -4y + y2 = 16 + 4

Combine like terms: 16 + 4 = 20
4 + -4y + y2 = 20

Factor a perfect square on the left side:
(y + -2)(y + -2) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(y + -2) equal to 4.472135955 and -4.472135955.


Subproblem 1
y + -2 = 4.472135955

Simplifying
y + -2 = 4.472135955

Reorder the terms:
-2 + y = 4.472135955

Solving
-2 + y = 4.472135955

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 = 4.472135955 + 2

Combine like terms: -2 + 2 = 0
0 + y = 4.472135955 + 2
y = 4.472135955 + 2

Combine like terms: 4.472135955 + 2 = 6.472135955
y = 6.472135955

Simplifying
y = 6.472135955


Subproblem 2
y + -2 = -4.472135955

Simplifying
y + -2 = -4.472135955

Reorder the terms:
-2 + y = -4.472135955

Solving
-2 + y = -4.472135955

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 = -4.472135955 + 2

Combine like terms: -2 + 2 = 0
0 + y = -4.472135955 + 2
y = -4.472135955 + 2

Combine like terms: -4.472135955 + 2 = -2.472135955
y = -2.472135955

Simplifying
y = -2.472135955


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {6.472135955, -2.472135955}

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