100(t^2)+40t-1=0

Solution for 100(t^2)+40t-1=0 equation:

Simplifying
100(t2) + 40t + -1 = 0

Reorder the terms:
-1 + 40t + 100t2 = 0

Solving
-1 + 40t + 100t2 = 0

Solving for variable 't'.

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

Divide each side by '100'.
-0.01 + 0.4t + t2 = 0

Move the constant term to the right:

Add '0.01' to each side of the equation.
-0.01 + 0.4t + 0.01 + t2 = 0 + 0.01

Reorder the terms:
-0.01 + 0.01 + 0.4t + t2 = 0 + 0.01

Combine like terms: -0.01 + 0.01 = 0.00
0.00 + 0.4t + t2 = 0 + 0.01
0.4t + t2 = 0 + 0.01

Combine like terms: 0 + 0.01 = 0.01
0.4t + t2 = 0.01

The t term is 0.4t.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4t + 0.04 + t2 = 0.01 + 0.04

Reorder the terms:
0.04 + 0.4t + t2 = 0.01 + 0.04

Combine like terms: 0.01 + 0.04 = 0.05
0.04 + 0.4t + t2 = 0.05

Factor a perfect square on the left side:
(t + 0.2)(t + 0.2) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(t + 0.2) equal to 0.223606798 and -0.223606798.

Subproblem 1
t + 0.2 = 0.223606798

Simplifying
t + 0.2 = 0.223606798

Reorder the terms:
0.2 + t = 0.223606798

Solving
0.2 + t = 0.223606798

Solving for variable 't'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + t = 0.223606798 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + t = 0.223606798 + -0.2
t = 0.223606798 + -0.2

Combine like terms: 0.223606798 + -0.2 = 0.023606798
t = 0.023606798

Simplifying
t = 0.023606798

Subproblem 2
t + 0.2 = -0.223606798

Simplifying
t + 0.2 = -0.223606798

Reorder the terms:
0.2 + t = -0.223606798

Solving
0.2 + t = -0.223606798

Solving for variable 't'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + t = -0.223606798 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + t = -0.223606798 + -0.2
t = -0.223606798 + -0.2

Combine like terms: -0.223606798 + -0.2 = -0.423606798
t = -0.423606798

Simplifying
t = -0.423606798

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.023606798, -0.423606798}