0=-4.9t^2-9.8t+73.5

Solution for 0=-4.9t^2-9.8t+73.5 equation:

Simplifying
0 = -4.9t2 + -9.8t + 73.5

Reorder the terms:
0 = 73.5 + -9.8t + -4.9t2

Solving
0 = 73.5 + -9.8t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + -73.5 = -73.5
-73.5 + 9.8t + 4.9t2 = 73.5 + -9.8t + -4.9t2 + -73.5 + 9.8t + 4.9t2

Reorder the terms:
-73.5 + 9.8t + 4.9t2 = 73.5 + -73.5 + -9.8t + 9.8t + -4.9t2 + 4.9t2

Combine like terms: 73.5 + -73.5 = 0.0
-73.5 + 9.8t + 4.9t2 = 0.0 + -9.8t + 9.8t + -4.9t2 + 4.9t2
-73.5 + 9.8t + 4.9t2 = -9.8t + 9.8t + -4.9t2 + 4.9t2

Combine like terms: -9.8t + 9.8t = 0.0
-73.5 + 9.8t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2
-73.5 + 9.8t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-73.5 + 9.8t + 4.9t2 = 0.0

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

Divide each side by '4.9'.
-15 + 2t + t2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 2t + 15 + t2 = 0 + 15

Reorder the terms:
-15 + 15 + 2t + t2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 2t + t2 = 0 + 15
2t + t2 = 0 + 15

Combine like terms: 0 + 15 = 15
2t + t2 = 15

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 = 15 + 1

Reorder the terms:
1 + 2t + t2 = 15 + 1

Combine like terms: 15 + 1 = 16
1 + 2t + t2 = 16

Factor a perfect square on the left side:
(t + 1)(t + 1) = 16

Calculate the square root of the right side: 4

Break this problem into two subproblems by setting 
(t + 1) equal to 4 and -4.

Subproblem 1
t + 1 = 4

Simplifying
t + 1 = 4

Reorder the terms:
1 + t = 4

Solving
1 + t = 4

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 = 4 + -1

Combine like terms: 1 + -1 = 0
0 + t = 4 + -1
t = 4 + -1

Combine like terms: 4 + -1 = 3
t = 3

Simplifying
t = 3

Subproblem 2
t + 1 = -4

Simplifying
t + 1 = -4

Reorder the terms:
1 + t = -4

Solving
1 + t = -4

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 = -4 + -1

Combine like terms: 1 + -1 = 0
0 + t = -4 + -1
t = -4 + -1

Combine like terms: -4 + -1 = -5
t = -5

Simplifying
t = -5

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3, -5}