t^2-2t-11=0

Solution for t^2-2t-11=0 equation:

Simplifying
t2 + -2t + -11 = 0

Reorder the terms:
-11 + -2t + t2 = 0

Solving
-11 + -2t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -2t + 11 + t2 = 0 + 11

Reorder the terms:
-11 + 11 + -2t + t2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2t + t2 = 0 + 11
-2t + t2 = 0 + 11

Combine like terms: 0 + 11 = 11
-2t + t2 = 11

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 = 11 + 1

Reorder the terms:
1 + -2t + t2 = 11 + 1

Combine like terms: 11 + 1 = 12
1 + -2t + t2 = 12

Factor a perfect square on the left side:
(t + -1)(t + -1) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(t + -1) equal to 3.464101615 and -3.464101615.

Subproblem 1
t + -1 = 3.464101615

Simplifying
t + -1 = 3.464101615

Reorder the terms:
-1 + t = 3.464101615

Solving
-1 + t = 3.464101615

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 = 3.464101615 + 1

Combine like terms: -1 + 1 = 0
0 + t = 3.464101615 + 1
t = 3.464101615 + 1

Combine like terms: 3.464101615 + 1 = 4.464101615
t = 4.464101615

Simplifying
t = 4.464101615

Subproblem 2
t + -1 = -3.464101615

Simplifying
t + -1 = -3.464101615

Reorder the terms:
-1 + t = -3.464101615

Solving
-1 + t = -3.464101615

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 = -3.464101615 + 1

Combine like terms: -1 + 1 = 0
0 + t = -3.464101615 + 1
t = -3.464101615 + 1

Combine like terms: -3.464101615 + 1 = -2.464101615
t = -2.464101615

Simplifying
t = -2.464101615

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.464101615, -2.464101615}