t^2-4.5t+3.5=0

Solution for t^2-4.5t+3.5=0 equation:

Simplifying
t2 + -4.5t + 3.5 = 0

Reorder the terms:
3.5 + -4.5t + t2 = 0

Solving
3.5 + -4.5t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-3.5' to each side of the equation.
3.5 + -4.5t + -3.5 + t2 = 0 + -3.5

Reorder the terms:
3.5 + -3.5 + -4.5t + t2 = 0 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + -4.5t + t2 = 0 + -3.5
-4.5t + t2 = 0 + -3.5

Combine like terms: 0 + -3.5 = -3.5
-4.5t + t2 = -3.5

The t term is -4.5t.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5t + 5.0625 + t2 = -3.5 + 5.0625

Reorder the terms:
5.0625 + -4.5t + t2 = -3.5 + 5.0625

Combine like terms: -3.5 + 5.0625 = 1.5625
5.0625 + -4.5t + t2 = 1.5625

Factor a perfect square on the left side:
(t + -2.25)(t + -2.25) = 1.5625

Calculate the square root of the right side: 1.25

Break this problem into two subproblems by setting 
(t + -2.25) equal to 1.25 and -1.25.

Subproblem 1
t + -2.25 = 1.25

Simplifying
t + -2.25 = 1.25

Reorder the terms:
-2.25 + t = 1.25

Solving
-2.25 + t = 1.25

Solving for variable 't'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + t = 1.25 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + t = 1.25 + 2.25
t = 1.25 + 2.25

Combine like terms: 1.25 + 2.25 = 3.5
t = 3.5

Simplifying
t = 3.5

Subproblem 2
t + -2.25 = -1.25

Simplifying
t + -2.25 = -1.25

Reorder the terms:
-2.25 + t = -1.25

Solving
-2.25 + t = -1.25

Solving for variable 't'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + t = -1.25 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + t = -1.25 + 2.25
t = -1.25 + 2.25

Combine like terms: -1.25 + 2.25 = 1
t = 1

Simplifying
t = 1

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.5, 1}