t^2-11t+3=0

Solution for t^2-11t+3=0 equation:

Simplifying
t2 + -11t + 3 = 0

Reorder the terms:
3 + -11t + t2 = 0

Solving
3 + -11t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -11t + -3 + t2 = 0 + -3

Reorder the terms:
3 + -3 + -11t + t2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -11t + t2 = 0 + -3
-11t + t2 = 0 + -3

Combine like terms: 0 + -3 = -3
-11t + t2 = -3

The t term is -11t.  Take half its coefficient (-5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
-11t + 30.25 + t2 = -3 + 30.25

Reorder the terms:
30.25 + -11t + t2 = -3 + 30.25

Combine like terms: -3 + 30.25 = 27.25
30.25 + -11t + t2 = 27.25

Factor a perfect square on the left side:
(t + -5.5)(t + -5.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(t + -5.5) equal to 5.220153254 and -5.220153254.

Subproblem 1
t + -5.5 = 5.220153254

Simplifying
t + -5.5 = 5.220153254

Reorder the terms:
-5.5 + t = 5.220153254

Solving
-5.5 + t = 5.220153254

Solving for variable 't'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + t = 5.220153254 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + t = 5.220153254 + 5.5
t = 5.220153254 + 5.5

Combine like terms: 5.220153254 + 5.5 = 10.720153254
t = 10.720153254

Simplifying
t = 10.720153254

Subproblem 2
t + -5.5 = -5.220153254

Simplifying
t + -5.5 = -5.220153254

Reorder the terms:
-5.5 + t = -5.220153254

Solving
-5.5 + t = -5.220153254

Solving for variable 't'.

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

Add '5.5' to each side of the equation.
-5.5 + 5.5 + t = -5.220153254 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + t = -5.220153254 + 5.5
t = -5.220153254 + 5.5

Combine like terms: -5.220153254 + 5.5 = 0.279846746
t = 0.279846746

Simplifying
t = 0.279846746

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.720153254, 0.279846746}