0.2t^2-0.04t=0.03

Solution for 0.2t^2-0.04t=0.03 equation:

Simplifying
0.2t2 + -0.04t = 0.03

Reorder the terms:
-0.04t + 0.2t2 = 0.03

Solving
-0.04t + 0.2t2 = 0.03

Solving for variable 't'.

Reorder the terms:
-0.03 + -0.04t + 0.2t2 = 0.03 + -0.03

Combine like terms: 0.03 + -0.03 = 0.00
-0.03 + -0.04t + 0.2t2 = 0.00

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

Divide each side by '0.2'.
-0.15 + -0.2t + t2 = 0.0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + -0.2t + 0.15 + t2 = 0.0 + 0.15

Reorder the terms:
-0.15 + 0.15 + -0.2t + t2 = 0.0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + -0.2t + t2 = 0.0 + 0.15
-0.2t + t2 = 0.0 + 0.15

Combine like terms: 0.0 + 0.15 = 0.15
-0.2t + t2 = 0.15

The t term is -0.2t.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2t + 0.01 + t2 = 0.15 + 0.01

Reorder the terms:
0.01 + -0.2t + t2 = 0.15 + 0.01

Combine like terms: 0.15 + 0.01 = 0.16
0.01 + -0.2t + t2 = 0.16

Factor a perfect square on the left side:
(t + -0.1)(t + -0.1) = 0.16

Calculate the square root of the right side: 0.4

Break this problem into two subproblems by setting 
(t + -0.1) equal to 0.4 and -0.4.

Subproblem 1
t + -0.1 = 0.4

Simplifying
t + -0.1 = 0.4

Reorder the terms:
-0.1 + t = 0.4

Solving
-0.1 + t = 0.4

Solving for variable 't'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + t = 0.4 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + t = 0.4 + 0.1
t = 0.4 + 0.1

Combine like terms: 0.4 + 0.1 = 0.5
t = 0.5

Simplifying
t = 0.5

Subproblem 2
t + -0.1 = -0.4

Simplifying
t + -0.1 = -0.4

Reorder the terms:
-0.1 + t = -0.4

Solving
-0.1 + t = -0.4

Solving for variable 't'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + t = -0.4 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + t = -0.4 + 0.1
t = -0.4 + 0.1

Combine like terms: -0.4 + 0.1 = -0.3
t = -0.3

Simplifying
t = -0.3

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.5, -0.3}