20t+40t^2=100

Solution for 20t+40t^2=100 equation:

Simplifying
20t + 40t2 = 100

Solving
20t + 40t2 = 100

Solving for variable 't'.

Reorder the terms:
-100 + 20t + 40t2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 20t + 40t2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-5 + t + 2t2) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-5 + t + 2t2)' equal to zero and attempt to solve:

Simplifying
-5 + t + 2t2 = 0

Solving
-5 + t + 2t2 = 0

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

Divide each side by '2'.
-2.5 + 0.5t + t2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 0.5t + 2.5 + t2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 0.5t + t2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 0.5t + t2 = 0 + 2.5
0.5t + t2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
0.5t + t2 = 2.5

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.5t + 0.25 + t2 = 2.5 + 0.25

Reorder the terms:
0.25 + 0.5t + t2 = 2.5 + 0.25

Combine like terms: 2.5 + 0.25 = 2.75
0.25 + 0.5t + t2 = 2.75

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 2.75

Calculate the square root of the right side: 1.658312395

Break this problem into two subproblems by setting 
(t + 0.5) equal to 1.658312395 and -1.658312395.

Subproblem 1
t + 0.5 = 1.658312395

Simplifying
t + 0.5 = 1.658312395

Reorder the terms:
0.5 + t = 1.658312395

Solving
0.5 + t = 1.658312395

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 1.658312395 + -0.5
t = 1.658312395 + -0.5

Combine like terms: 1.658312395 + -0.5 = 1.158312395
t = 1.158312395

Simplifying
t = 1.158312395

Subproblem 2
t + 0.5 = -1.658312395

Simplifying
t + 0.5 = -1.658312395

Reorder the terms:
0.5 + t = -1.658312395

Solving
0.5 + t = -1.658312395

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -1.658312395 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -1.658312395 + -0.5
t = -1.658312395 + -0.5

Combine like terms: -1.658312395 + -0.5 = -2.158312395
t = -2.158312395

Simplifying
t = -2.158312395

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.158312395, -2.158312395}
Solution
t = {1.158312395, -2.158312395}