0=217-17t-16t^2

Solution for 0=217-17t-16t^2 equation:

Simplifying
0 = 217 + -17t + -16t2

Solving
0 = 217 + -17t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -217 = -217
-217 + 17t + 16t2 = 217 + -17t + -16t2 + -217 + 17t + 16t2

Reorder the terms:
-217 + 17t + 16t2 = 217 + -217 + -17t + 17t + -16t2 + 16t2

Combine like terms: 217 + -217 = 0
-217 + 17t + 16t2 = 0 + -17t + 17t + -16t2 + 16t2
-217 + 17t + 16t2 = -17t + 17t + -16t2 + 16t2

Combine like terms: -17t + 17t = 0
-217 + 17t + 16t2 = 0 + -16t2 + 16t2
-217 + 17t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-217 + 17t + 16t2 = 0

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

Divide each side by '16'.
-13.5625 + 1.0625t + t2 = 0

Move the constant term to the right:

Add '13.5625' to each side of the equation.
-13.5625 + 1.0625t + 13.5625 + t2 = 0 + 13.5625

Reorder the terms:
-13.5625 + 13.5625 + 1.0625t + t2 = 0 + 13.5625

Combine like terms: -13.5625 + 13.5625 = 0.0000
0.0000 + 1.0625t + t2 = 0 + 13.5625
1.0625t + t2 = 0 + 13.5625

Combine like terms: 0 + 13.5625 = 13.5625
1.0625t + t2 = 13.5625

The t term is 1.0625t.  Take half its coefficient (0.53125).
Square it (0.2822265625) and add it to both sides.

Add '0.2822265625' to each side of the equation.
1.0625t + 0.2822265625 + t2 = 13.5625 + 0.2822265625

Reorder the terms:
0.2822265625 + 1.0625t + t2 = 13.5625 + 0.2822265625

Combine like terms: 13.5625 + 0.2822265625 = 13.8447265625
0.2822265625 + 1.0625t + t2 = 13.8447265625

Factor a perfect square on the left side:
(t + 0.53125)(t + 0.53125) = 13.8447265625

Calculate the square root of the right side: 3.720850247

Break this problem into two subproblems by setting 
(t + 0.53125) equal to 3.720850247 and -3.720850247.

Subproblem 1
t + 0.53125 = 3.720850247

Simplifying
t + 0.53125 = 3.720850247

Reorder the terms:
0.53125 + t = 3.720850247

Solving
0.53125 + t = 3.720850247

Solving for variable 't'.

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

Add '-0.53125' to each side of the equation.
0.53125 + -0.53125 + t = 3.720850247 + -0.53125

Combine like terms: 0.53125 + -0.53125 = 0.00000
0.00000 + t = 3.720850247 + -0.53125
t = 3.720850247 + -0.53125

Combine like terms: 3.720850247 + -0.53125 = 3.189600247
t = 3.189600247

Simplifying
t = 3.189600247

Subproblem 2
t + 0.53125 = -3.720850247

Simplifying
t + 0.53125 = -3.720850247

Reorder the terms:
0.53125 + t = -3.720850247

Solving
0.53125 + t = -3.720850247

Solving for variable 't'.

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

Add '-0.53125' to each side of the equation.
0.53125 + -0.53125 + t = -3.720850247 + -0.53125

Combine like terms: 0.53125 + -0.53125 = 0.00000
0.00000 + t = -3.720850247 + -0.53125
t = -3.720850247 + -0.53125

Combine like terms: -3.720850247 + -0.53125 = -4.252100247
t = -4.252100247

Simplifying
t = -4.252100247

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.189600247, -4.252100247}