-22t-9.81t^2=-10

Solution for -22t-9.81t^2=-10 equation:

Simplifying
-22t + -9.81t2 = -10

Solving
-22t + -9.81t2 = -10

Solving for variable 't'.

Reorder the terms:
10 + -22t + -9.81t2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -22t + -9.81t2 = 0

Begin completing the square.  Divide all terms by
-9.81 the coefficient of the squared term: 

Divide each side by '-9.81'.
-1.019367992 + 2.242609582t + t2 = 0

Move the constant term to the right:

Add '1.019367992' to each side of the equation.
-1.019367992 + 2.242609582t + 1.019367992 + t2 = 0 + 1.019367992

Reorder the terms:
-1.019367992 + 1.019367992 + 2.242609582t + t2 = 0 + 1.019367992

Combine like terms: -1.019367992 + 1.019367992 = 0.000000000
0.000000000 + 2.242609582t + t2 = 0 + 1.019367992
2.242609582t + t2 = 0 + 1.019367992

Combine like terms: 0 + 1.019367992 = 1.019367992
2.242609582t + t2 = 1.019367992

The t term is 2.242609582t.  Take half its coefficient (1.121304791).
Square it (1.257324434) and add it to both sides.

Add '1.257324434' to each side of the equation.
2.242609582t + 1.257324434 + t2 = 1.019367992 + 1.257324434

Reorder the terms:
1.257324434 + 2.242609582t + t2 = 1.019367992 + 1.257324434

Combine like terms: 1.019367992 + 1.257324434 = 2.276692426
1.257324434 + 2.242609582t + t2 = 2.276692426

Factor a perfect square on the left side:
(t + 1.121304791)(t + 1.121304791) = 2.276692426

Calculate the square root of the right side: 1.508871242

Break this problem into two subproblems by setting 
(t + 1.121304791) equal to 1.508871242 and -1.508871242.

Subproblem 1
t + 1.121304791 = 1.508871242

Simplifying
t + 1.121304791 = 1.508871242

Reorder the terms:
1.121304791 + t = 1.508871242

Solving
1.121304791 + t = 1.508871242

Solving for variable 't'.

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

Add '-1.121304791' to each side of the equation.
1.121304791 + -1.121304791 + t = 1.508871242 + -1.121304791

Combine like terms: 1.121304791 + -1.121304791 = 0.000000000
0.000000000 + t = 1.508871242 + -1.121304791
t = 1.508871242 + -1.121304791

Combine like terms: 1.508871242 + -1.121304791 = 0.387566451
t = 0.387566451

Simplifying
t = 0.387566451

Subproblem 2
t + 1.121304791 = -1.508871242

Simplifying
t + 1.121304791 = -1.508871242

Reorder the terms:
1.121304791 + t = -1.508871242

Solving
1.121304791 + t = -1.508871242

Solving for variable 't'.

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

Add '-1.121304791' to each side of the equation.
1.121304791 + -1.121304791 + t = -1.508871242 + -1.121304791

Combine like terms: 1.121304791 + -1.121304791 = 0.000000000
0.000000000 + t = -1.508871242 + -1.121304791
t = -1.508871242 + -1.121304791

Combine like terms: -1.508871242 + -1.121304791 = -2.630176033
t = -2.630176033

Simplifying
t = -2.630176033

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.387566451, -2.630176033}