0=4.91t^2+65.96t-451.74

Solution for 0=4.91t^2+65.96t-451.74 equation:

Simplifying
0 = 4.91t2 + 65.96t + -451.74

Reorder the terms:
0 = -451.74 + 65.96t + 4.91t2

Solving
0 = -451.74 + 65.96t + 4.91t2

Solving for variable 't'.

Combine like terms: 0 + 451.74 = 451.74
451.74 + -65.96t + -4.91t2 = -451.74 + 65.96t + 4.91t2 + 451.74 + -65.96t + -4.91t2

Reorder the terms:
451.74 + -65.96t + -4.91t2 = -451.74 + 451.74 + 65.96t + -65.96t + 4.91t2 + -4.91t2

Combine like terms: -451.74 + 451.74 = 0.00
451.74 + -65.96t + -4.91t2 = 0.00 + 65.96t + -65.96t + 4.91t2 + -4.91t2
451.74 + -65.96t + -4.91t2 = 65.96t + -65.96t + 4.91t2 + -4.91t2

Combine like terms: 65.96t + -65.96t = 0.00
451.74 + -65.96t + -4.91t2 = 0.00 + 4.91t2 + -4.91t2
451.74 + -65.96t + -4.91t2 = 4.91t2 + -4.91t2

Combine like terms: 4.91t2 + -4.91t2 = 0.00
451.74 + -65.96t + -4.91t2 = 0.00

Begin completing the square.  Divide all terms by
-4.91 the coefficient of the squared term: 

Divide each side by '-4.91'.
-92.00407332 + 13.43380855t + t2 = 0

Move the constant term to the right:

Add '92.00407332' to each side of the equation.
-92.00407332 + 13.43380855t + 92.00407332 + t2 = 0 + 92.00407332

Reorder the terms:
-92.00407332 + 92.00407332 + 13.43380855t + t2 = 0 + 92.00407332

Combine like terms: -92.00407332 + 92.00407332 = 0.00000000
0.00000000 + 13.43380855t + t2 = 0 + 92.00407332
13.43380855t + t2 = 0 + 92.00407332

Combine like terms: 0 + 92.00407332 = 92.00407332
13.43380855t + t2 = 92.00407332

The t term is 13.43380855t.  Take half its coefficient (6.716904275).
Square it (45.11680304) and add it to both sides.

Add '45.11680304' to each side of the equation.
13.43380855t + 45.11680304 + t2 = 92.00407332 + 45.11680304

Reorder the terms:
45.11680304 + 13.43380855t + t2 = 92.00407332 + 45.11680304

Combine like terms: 92.00407332 + 45.11680304 = 137.12087636
45.11680304 + 13.43380855t + t2 = 137.12087636

Factor a perfect square on the left side:
(t + 6.716904275)(t + 6.716904275) = 137.12087636

Calculate the square root of the right side: 11.709862354

Break this problem into two subproblems by setting 
(t + 6.716904275) equal to 11.709862354 and -11.709862354.

Subproblem 1
t + 6.716904275 = 11.709862354

Simplifying
t + 6.716904275 = 11.709862354

Reorder the terms:
6.716904275 + t = 11.709862354

Solving
6.716904275 + t = 11.709862354

Solving for variable 't'.

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

Add '-6.716904275' to each side of the equation.
6.716904275 + -6.716904275 + t = 11.709862354 + -6.716904275

Combine like terms: 6.716904275 + -6.716904275 = 0.000000000
0.000000000 + t = 11.709862354 + -6.716904275
t = 11.709862354 + -6.716904275

Combine like terms: 11.709862354 + -6.716904275 = 4.992958079
t = 4.992958079

Simplifying
t = 4.992958079

Subproblem 2
t + 6.716904275 = -11.709862354

Simplifying
t + 6.716904275 = -11.709862354

Reorder the terms:
6.716904275 + t = -11.709862354

Solving
6.716904275 + t = -11.709862354

Solving for variable 't'.

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

Add '-6.716904275' to each side of the equation.
6.716904275 + -6.716904275 + t = -11.709862354 + -6.716904275

Combine like terms: 6.716904275 + -6.716904275 = 0.000000000
0.000000000 + t = -11.709862354 + -6.716904275
t = -11.709862354 + -6.716904275

Combine like terms: -11.709862354 + -6.716904275 = -18.426766629
t = -18.426766629

Simplifying
t = -18.426766629

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.992958079, -18.426766629}