(-5t^2)-10t-1=0

Solution for (-5t^2)-10t-1=0 equation:

Simplifying
(-5t2) + -10t + -1 = 0

Reorder the terms:
-1 + -10t + (-5t2) = 0

Solving
-1 + -10t + (-5t2) = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 10t + (5t2)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 10t + (5t2))' equal to zero and attempt to solve:

Simplifying
1 + 10t + (5t2) = 0

Solving
1 + 10t + (5t2) = 0

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

Divide each side by '5'.
0.2 + 2t + t2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2t + -0.2 + t2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2t + t2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2t + t2 = 0 + -0.2
2t + t2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2t + t2 = -0.2

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 = -0.2 + 1

Reorder the terms:
1 + 2t + t2 = -0.2 + 1

Combine like terms: -0.2 + 1 = 0.8
1 + 2t + t2 = 0.8

Factor a perfect square on the left side:
((t) + 1)((t) + 1) = 0.8

Calculate the square root of the right side: 0.894427191

Break this problem into two subproblems by setting 
((t) + 1) equal to 0.894427191 and -0.894427191.

Subproblem 1
(t) + 1 = 0.894427191

Simplifying
(t) + 1 = 0.894427191
t + 1 = 0.894427191

Reorder the terms:
1 + t = 0.894427191

Solving
1 + t = 0.894427191

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 = 0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + t = 0.894427191 + -1
t = 0.894427191 + -1

Combine like terms: 0.894427191 + -1 = -0.105572809
t = -0.105572809

Simplifying
t = -0.105572809

Subproblem 2
(t) + 1 = -0.894427191

Simplifying
(t) + 1 = -0.894427191
t + 1 = -0.894427191

Reorder the terms:
1 + t = -0.894427191

Solving
1 + t = -0.894427191

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 = -0.894427191 + -1

Combine like terms: 1 + -1 = 0
0 + t = -0.894427191 + -1
t = -0.894427191 + -1

Combine like terms: -0.894427191 + -1 = -1.894427191
t = -1.894427191

Simplifying
t = -1.894427191

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.105572809, -1.894427191}
Solution
t = {-0.105572809, -1.894427191}