0=t^2-9t+5

Solution for 0=t^2-9t+5 equation:

Simplifying
0 = t2 + -9t + 5

Reorder the terms:
0 = 5 + -9t + t2

Solving
0 = 5 + -9t + t2

Solving for variable 't'.

Combine like terms: 0 + -5 = -5
-5 + 9t + -1t2 = 5 + -9t + t2 + -5 + 9t + -1t2

Reorder the terms:
-5 + 9t + -1t2 = 5 + -5 + -9t + 9t + t2 + -1t2

Combine like terms: 5 + -5 = 0
-5 + 9t + -1t2 = 0 + -9t + 9t + t2 + -1t2
-5 + 9t + -1t2 = -9t + 9t + t2 + -1t2

Combine like terms: -9t + 9t = 0
-5 + 9t + -1t2 = 0 + t2 + -1t2
-5 + 9t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-5 + 9t + -1t2 = 0

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

Divide each side by '-1'.
5 + -9t + t2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -9t + -5 + t2 = 0 + -5

Reorder the terms:
5 + -5 + -9t + t2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -9t + t2 = 0 + -5
-9t + t2 = 0 + -5

Combine like terms: 0 + -5 = -5
-9t + t2 = -5

The t term is -9t.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9t + 20.25 + t2 = -5 + 20.25

Reorder the terms:
20.25 + -9t + t2 = -5 + 20.25

Combine like terms: -5 + 20.25 = 15.25
20.25 + -9t + t2 = 15.25

Factor a perfect square on the left side:
(t + -4.5)(t + -4.5) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(t + -4.5) equal to 3.905124838 and -3.905124838.

Subproblem 1
t + -4.5 = 3.905124838

Simplifying
t + -4.5 = 3.905124838

Reorder the terms:
-4.5 + t = 3.905124838

Solving
-4.5 + t = 3.905124838

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = 3.905124838 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = 3.905124838 + 4.5
t = 3.905124838 + 4.5

Combine like terms: 3.905124838 + 4.5 = 8.405124838
t = 8.405124838

Simplifying
t = 8.405124838

Subproblem 2
t + -4.5 = -3.905124838

Simplifying
t + -4.5 = -3.905124838

Reorder the terms:
-4.5 + t = -3.905124838

Solving
-4.5 + t = -3.905124838

Solving for variable 't'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + t = -3.905124838 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + t = -3.905124838 + 4.5
t = -3.905124838 + 4.5

Combine like terms: -3.905124838 + 4.5 = 0.594875162
t = 0.594875162

Simplifying
t = 0.594875162

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {8.405124838, 0.594875162}