0=-0.5(9.8)t^2+10t+2

Solution for 0=-0.5(9.8)t^2+10t+2 equation:

Simplifying
0 = -0.5(9.8) * t2 + 10t + 2

Multiply -0.5 * 9.8
0 = -4.9t2 + 10t + 2

Reorder the terms:
0 = 2 + 10t + -4.9t2

Solving
0 = 2 + 10t + -4.9t2

Solving for variable 't'.

Combine like terms: 0 + -2 = -2
-2 + -10t + 4.9t2 = 2 + 10t + -4.9t2 + -2 + -10t + 4.9t2

Reorder the terms:
-2 + -10t + 4.9t2 = 2 + -2 + 10t + -10t + -4.9t2 + 4.9t2

Combine like terms: 2 + -2 = 0
-2 + -10t + 4.9t2 = 0 + 10t + -10t + -4.9t2 + 4.9t2
-2 + -10t + 4.9t2 = 10t + -10t + -4.9t2 + 4.9t2

Combine like terms: 10t + -10t = 0
-2 + -10t + 4.9t2 = 0 + -4.9t2 + 4.9t2
-2 + -10t + 4.9t2 = -4.9t2 + 4.9t2

Combine like terms: -4.9t2 + 4.9t2 = 0.0
-2 + -10t + 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'.
-0.4081632653 + -2.040816327t + t2 = 0

Move the constant term to the right:

Add '0.4081632653' to each side of the equation.
-0.4081632653 + -2.040816327t + 0.4081632653 + t2 = 0 + 0.4081632653

Reorder the terms:
-0.4081632653 + 0.4081632653 + -2.040816327t + t2 = 0 + 0.4081632653

Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000
0.0000000000 + -2.040816327t + t2 = 0 + 0.4081632653
-2.040816327t + t2 = 0 + 0.4081632653

Combine like terms: 0 + 0.4081632653 = 0.4081632653
-2.040816327t + t2 = 0.4081632653

The t term is -2.040816327t.  Take half its coefficient (-1.020408164).
Square it (1.041232821) and add it to both sides.

Add '1.041232821' to each side of the equation.
-2.040816327t + 1.041232821 + t2 = 0.4081632653 + 1.041232821

Reorder the terms:
1.041232821 + -2.040816327t + t2 = 0.4081632653 + 1.041232821

Combine like terms: 0.4081632653 + 1.041232821 = 1.4493960863
1.041232821 + -2.040816327t + t2 = 1.4493960863

Factor a perfect square on the left side:
(t + -1.020408164)(t + -1.020408164) = 1.4493960863

Calculate the square root of the right side: 1.20390867

Break this problem into two subproblems by setting 
(t + -1.020408164) equal to 1.20390867 and -1.20390867.

Subproblem 1
t + -1.020408164 = 1.20390867

Simplifying
t + -1.020408164 = 1.20390867

Reorder the terms:
-1.020408164 + t = 1.20390867

Solving
-1.020408164 + t = 1.20390867

Solving for variable 't'.

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

Add '1.020408164' to each side of the equation.
-1.020408164 + 1.020408164 + t = 1.20390867 + 1.020408164

Combine like terms: -1.020408164 + 1.020408164 = 0.000000000
0.000000000 + t = 1.20390867 + 1.020408164
t = 1.20390867 + 1.020408164

Combine like terms: 1.20390867 + 1.020408164 = 2.224316834
t = 2.224316834

Simplifying
t = 2.224316834

Subproblem 2
t + -1.020408164 = -1.20390867

Simplifying
t + -1.020408164 = -1.20390867

Reorder the terms:
-1.020408164 + t = -1.20390867

Solving
-1.020408164 + t = -1.20390867

Solving for variable 't'.

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

Add '1.020408164' to each side of the equation.
-1.020408164 + 1.020408164 + t = -1.20390867 + 1.020408164

Combine like terms: -1.020408164 + 1.020408164 = 0.000000000
0.000000000 + t = -1.20390867 + 1.020408164
t = -1.20390867 + 1.020408164

Combine like terms: -1.20390867 + 1.020408164 = -0.183500506
t = -0.183500506

Simplifying
t = -0.183500506

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.224316834, -0.183500506}