4.9t^2-200t+500=0

Solution for 4.9t^2-200t+500=0 equation:

Simplifying
4.9t2 + -200t + 500 = 0

Reorder the terms:
500 + -200t + 4.9t2 = 0

Solving
500 + -200t + 4.9t2 = 0

Solving for variable 't'.

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

Divide each side by '4.9'.
102.0408163 + -40.81632653t + t2 = 0

Move the constant term to the right:

Add '-102.0408163' to each side of the equation.
102.0408163 + -40.81632653t + -102.0408163 + t2 = 0 + -102.0408163

Reorder the terms:
102.0408163 + -102.0408163 + -40.81632653t + t2 = 0 + -102.0408163

Combine like terms: 102.0408163 + -102.0408163 = 0.0000000
0.0000000 + -40.81632653t + t2 = 0 + -102.0408163
-40.81632653t + t2 = 0 + -102.0408163

Combine like terms: 0 + -102.0408163 = -102.0408163
-40.81632653t + t2 = -102.0408163

The t term is -40.81632653t.  Take half its coefficient (-20.40816327).
Square it (416.4931281) and add it to both sides.

Add '416.4931281' to each side of the equation.
-40.81632653t + 416.4931281 + t2 = -102.0408163 + 416.4931281

Reorder the terms:
416.4931281 + -40.81632653t + t2 = -102.0408163 + 416.4931281

Combine like terms: -102.0408163 + 416.4931281 = 314.4523118
416.4931281 + -40.81632653t + t2 = 314.4523118

Factor a perfect square on the left side:
(t + -20.40816327)(t + -20.40816327) = 314.4523118

Calculate the square root of the right side: 17.73280327

Break this problem into two subproblems by setting 
(t + -20.40816327) equal to 17.73280327 and -17.73280327.

Subproblem 1
t + -20.40816327 = 17.73280327

Simplifying
t + -20.40816327 = 17.73280327

Reorder the terms:
-20.40816327 + t = 17.73280327

Solving
-20.40816327 + t = 17.73280327

Solving for variable 't'.

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

Add '20.40816327' to each side of the equation.
-20.40816327 + 20.40816327 + t = 17.73280327 + 20.40816327

Combine like terms: -20.40816327 + 20.40816327 = 0.00000000
0.00000000 + t = 17.73280327 + 20.40816327
t = 17.73280327 + 20.40816327

Combine like terms: 17.73280327 + 20.40816327 = 38.14096654
t = 38.14096654

Simplifying
t = 38.14096654

Subproblem 2
t + -20.40816327 = -17.73280327

Simplifying
t + -20.40816327 = -17.73280327

Reorder the terms:
-20.40816327 + t = -17.73280327

Solving
-20.40816327 + t = -17.73280327

Solving for variable 't'.

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

Add '20.40816327' to each side of the equation.
-20.40816327 + 20.40816327 + t = -17.73280327 + 20.40816327

Combine like terms: -20.40816327 + 20.40816327 = 0.00000000
0.00000000 + t = -17.73280327 + 20.40816327
t = -17.73280327 + 20.40816327

Combine like terms: -17.73280327 + 20.40816327 = 2.67536
t = 2.67536

Simplifying
t = 2.67536

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {38.14096654, 2.67536}