-0.08t^2+1.6t+20=0

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Solution for -0.08t^2+1.6t+20=0 equation:


Simplifying
-0.08t2 + 1.6t + 20 = 0

Reorder the terms:
20 + 1.6t + -0.08t2 = 0

Solving
20 + 1.6t + -0.08t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-0.08 the coefficient of the squared term: 

Divide each side by '-0.08'.
-250 + -20t + t2 = 0

Move the constant term to the right:

Add '250' to each side of the equation.
-250 + -20t + 250 + t2 = 0 + 250

Reorder the terms:
-250 + 250 + -20t + t2 = 0 + 250

Combine like terms: -250 + 250 = 0
0 + -20t + t2 = 0 + 250
-20t + t2 = 0 + 250

Combine like terms: 0 + 250 = 250
-20t + t2 = 250

The t term is -20t.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20t + 100 + t2 = 250 + 100

Reorder the terms:
100 + -20t + t2 = 250 + 100

Combine like terms: 250 + 100 = 350
100 + -20t + t2 = 350

Factor a perfect square on the left side:
(t + -10)(t + -10) = 350

Calculate the square root of the right side: 18.708286934

Break this problem into two subproblems by setting 
(t + -10) equal to 18.708286934 and -18.708286934.

Subproblem 1

t + -10 = 18.708286934 Simplifying t + -10 = 18.708286934 Reorder the terms: -10 + t = 18.708286934 Solving -10 + t = 18.708286934 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 18.708286934 + 10 Combine like terms: -10 + 10 = 0 0 + t = 18.708286934 + 10 t = 18.708286934 + 10 Combine like terms: 18.708286934 + 10 = 28.708286934 t = 28.708286934 Simplifying t = 28.708286934

Subproblem 2

t + -10 = -18.708286934 Simplifying t + -10 = -18.708286934 Reorder the terms: -10 + t = -18.708286934 Solving -10 + t = -18.708286934 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -18.708286934 + 10 Combine like terms: -10 + 10 = 0 0 + t = -18.708286934 + 10 t = -18.708286934 + 10 Combine like terms: -18.708286934 + 10 = -8.708286934 t = -8.708286934 Simplifying t = -8.708286934

Solution

The solution to the problem is based on the solutions from the subproblems. t = {28.708286934, -8.708286934}

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