0.2t^2+0.04t=0.03

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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 = 0.3
t = 0.3

Simplifying
t = 0.3


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 = -0.5
t = -0.5

Simplifying
t = -0.5


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

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