0=t^2+4.5t-2

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

Simplifying
0 = t2 + 4.5t + -2

Reorder the terms:
0 = -2 + 4.5t + t2

Solving
0 = -2 + 4.5t + t2

Solving for variable 't'.

Combine like terms: 0 + 2 = 2
2 + -4.5t + -1t2 = -2 + 4.5t + t2 + 2 + -4.5t + -1t2

Reorder the terms:
2 + -4.5t + -1t2 = -2 + 2 + 4.5t + -4.5t + t2 + -1t2

Combine like terms: -2 + 2 = 0
2 + -4.5t + -1t2 = 0 + 4.5t + -4.5t + t2 + -1t2
2 + -4.5t + -1t2 = 4.5t + -4.5t + t2 + -1t2

Combine like terms: 4.5t + -4.5t = 0.0
2 + -4.5t + -1t2 = 0.0 + t2 + -1t2
2 + -4.5t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
2 + -4.5t + -1t2 = 0

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

Divide each side by '-1'.
-2 + 4.5t + t2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 4.5t + 2 + t2 = 0 + 2

Reorder the terms:
-2 + 2 + 4.5t + t2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 4.5t + t2 = 0 + 2
4.5t + t2 = 0 + 2

Combine like terms: 0 + 2 = 2
4.5t + t2 = 2

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 = 2 + 5.0625

Reorder the terms:
5.0625 + 4.5t + t2 = 2 + 5.0625

Combine like terms: 2 + 5.0625 = 7.0625
5.0625 + 4.5t + t2 = 7.0625

Factor a perfect square on the left side:
(t + 2.25)(t + 2.25) = 7.0625

Calculate the square root of the right side: 2.657536453

Break this problem into two subproblems by setting 
(t + 2.25) equal to 2.657536453 and -2.657536453.

Subproblem 1
t + 2.25 = 2.657536453

Simplifying
t + 2.25 = 2.657536453

Reorder the terms:
2.25 + t = 2.657536453

Solving
2.25 + t = 2.657536453

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 = 2.657536453 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = 2.657536453 + -2.25
t = 2.657536453 + -2.25

Combine like terms: 2.657536453 + -2.25 = 0.407536453
t = 0.407536453

Simplifying
t = 0.407536453

Subproblem 2
t + 2.25 = -2.657536453

Simplifying
t + 2.25 = -2.657536453

Reorder the terms:
2.25 + t = -2.657536453

Solving
2.25 + t = -2.657536453

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 = -2.657536453 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + t = -2.657536453 + -2.25
t = -2.657536453 + -2.25

Combine like terms: -2.657536453 + -2.25 = -4.907536453
t = -4.907536453

Simplifying
t = -4.907536453

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.407536453, -4.907536453}