0=t^2-2t-16

Solution for 0=t^2-2t-16 equation:

Simplifying
0 = t2 + -2t + -16

Reorder the terms:
0 = -16 + -2t + t2

Solving
0 = -16 + -2t + t2

Solving for variable 't'.

Combine like terms: 0 + 16 = 16
16 + 2t + -1t2 = -16 + -2t + t2 + 16 + 2t + -1t2

Reorder the terms:
16 + 2t + -1t2 = -16 + 16 + -2t + 2t + t2 + -1t2

Combine like terms: -16 + 16 = 0
16 + 2t + -1t2 = 0 + -2t + 2t + t2 + -1t2
16 + 2t + -1t2 = -2t + 2t + t2 + -1t2

Combine like terms: -2t + 2t = 0
16 + 2t + -1t2 = 0 + t2 + -1t2
16 + 2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
16 + 2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-16 + -2t + t2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -2t + 16 + t2 = 0 + 16

Reorder the terms:
-16 + 16 + -2t + t2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -2t + t2 = 0 + 16
-2t + t2 = 0 + 16

Combine like terms: 0 + 16 = 16
-2t + t2 = 16

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 16 + 1

Reorder the terms:
1 + -2t + t2 = 16 + 1

Combine like terms: 16 + 1 = 17
1 + -2t + t2 = 17

Factor a perfect square on the left side:
(t + -1)(t + -1) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(t + -1) equal to 4.123105626 and -4.123105626.

Subproblem 1
t + -1 = 4.123105626

Simplifying
t + -1 = 4.123105626

Reorder the terms:
-1 + t = 4.123105626

Solving
-1 + t = 4.123105626

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + t = 4.123105626 + 1
t = 4.123105626 + 1

Combine like terms: 4.123105626 + 1 = 5.123105626
t = 5.123105626

Simplifying
t = 5.123105626

Subproblem 2
t + -1 = -4.123105626

Simplifying
t + -1 = -4.123105626

Reorder the terms:
-1 + t = -4.123105626

Solving
-1 + t = -4.123105626

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -4.123105626 + 1

Combine like terms: -1 + 1 = 0
0 + t = -4.123105626 + 1
t = -4.123105626 + 1

Combine like terms: -4.123105626 + 1 = -3.123105626
t = -3.123105626

Simplifying
t = -3.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.123105626, -3.123105626}