5t^2+2t+0.1=0

Solution for 5t^2+2t+0.1=0 equation:

Simplifying
5t2 + 2t + 0.1 = 0

Reorder the terms:
0.1 + 2t + 5t2 = 0

Solving
0.1 + 2t + 5t2 = 0

Solving for variable 't'.

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

Divide each side by '5'.
0.02 + 0.4t + t2 = 0

Move the constant term to the right:

Add '-0.02' to each side of the equation.
0.02 + 0.4t + -0.02 + t2 = 0 + -0.02

Reorder the terms:
0.02 + -0.02 + 0.4t + t2 = 0 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
0.00 + 0.4t + t2 = 0 + -0.02
0.4t + t2 = 0 + -0.02

Combine like terms: 0 + -0.02 = -0.02
0.4t + t2 = -0.02

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 = -0.02 + 0.04

Reorder the terms:
0.04 + 0.4t + t2 = -0.02 + 0.04

Combine like terms: -0.02 + 0.04 = 0.02
0.04 + 0.4t + t2 = 0.02

Factor a perfect square on the left side:
(t + 0.2)(t + 0.2) = 0.02

Calculate the square root of the right side: 0.141421356

Break this problem into two subproblems by setting 
(t + 0.2) equal to 0.141421356 and -0.141421356.

Subproblem 1
t + 0.2 = 0.141421356

Simplifying
t + 0.2 = 0.141421356

Reorder the terms:
0.2 + t = 0.141421356

Solving
0.2 + t = 0.141421356

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 = 0.141421356 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + t = 0.141421356 + -0.2
t = 0.141421356 + -0.2

Combine like terms: 0.141421356 + -0.2 = -0.058578644
t = -0.058578644

Simplifying
t = -0.058578644

Subproblem 2
t + 0.2 = -0.141421356

Simplifying
t + 0.2 = -0.141421356

Reorder the terms:
0.2 + t = -0.141421356

Solving
0.2 + t = -0.141421356

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 = -0.141421356 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + t = -0.141421356 + -0.2
t = -0.141421356 + -0.2

Combine like terms: -0.141421356 + -0.2 = -0.341421356
t = -0.341421356

Simplifying
t = -0.341421356

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.058578644, -0.341421356}