t^2-2t-6=0

Solution for t^2-2t-6=0 equation:

Simplifying
t2 + -2t + -6 = 0

Reorder the terms:
-6 + -2t + t2 = 0

Solving
-6 + -2t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -2t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -2t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -2t + t2 = 0 + 6
-2t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-2t + t2 = 6

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 = 6 + 1

Reorder the terms:
1 + -2t + t2 = 6 + 1

Combine like terms: 6 + 1 = 7
1 + -2t + t2 = 7

Factor a perfect square on the left side:
(t + -1)(t + -1) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(t + -1) equal to 2.645751311 and -2.645751311.

Subproblem 1
t + -1 = 2.645751311

Simplifying
t + -1 = 2.645751311

Reorder the terms:
-1 + t = 2.645751311

Solving
-1 + t = 2.645751311

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 = 2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + t = 2.645751311 + 1
t = 2.645751311 + 1

Combine like terms: 2.645751311 + 1 = 3.645751311
t = 3.645751311

Simplifying
t = 3.645751311

Subproblem 2
t + -1 = -2.645751311

Simplifying
t + -1 = -2.645751311

Reorder the terms:
-1 + t = -2.645751311

Solving
-1 + t = -2.645751311

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 = -2.645751311 + 1

Combine like terms: -1 + 1 = 0
0 + t = -2.645751311 + 1
t = -2.645751311 + 1

Combine like terms: -2.645751311 + 1 = -1.645751311
t = -1.645751311

Simplifying
t = -1.645751311

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.645751311, -1.645751311}