16=-16t^2+35t

Solution for 16=-16t^2+35t equation:

Simplifying
16 = -16t2 + 35t

Reorder the terms:
16 = 35t + -16t2

Solving
16 = 35t + -16t2

Solving for variable 't'.

Reorder the terms:
16 + -35t + 16t2 = 35t + -35t + -16t2 + 16t2

Combine like terms: 35t + -35t = 0
16 + -35t + 16t2 = 0 + -16t2 + 16t2
16 + -35t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
16 + -35t + 16t2 = 0

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

Divide each side by '16'.
1 + -2.1875t + t2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -2.1875t + -1 + t2 = 0 + -1

Reorder the terms:
1 + -1 + -2.1875t + t2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2.1875t + t2 = 0 + -1
-2.1875t + t2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2.1875t + t2 = -1

The t term is -2.1875t.  Take half its coefficient (-1.09375).
Square it (1.196289063) and add it to both sides.

Add '1.196289063' to each side of the equation.
-2.1875t + 1.196289063 + t2 = -1 + 1.196289063

Reorder the terms:
1.196289063 + -2.1875t + t2 = -1 + 1.196289063

Combine like terms: -1 + 1.196289063 = 0.196289063
1.196289063 + -2.1875t + t2 = 0.196289063

Factor a perfect square on the left side:
(t + -1.09375)(t + -1.09375) = 0.196289063

Calculate the square root of the right side: 0.443045216

Break this problem into two subproblems by setting 
(t + -1.09375) equal to 0.443045216 and -0.443045216.

Subproblem 1
t + -1.09375 = 0.443045216

Simplifying
t + -1.09375 = 0.443045216

Reorder the terms:
-1.09375 + t = 0.443045216

Solving
-1.09375 + t = 0.443045216

Solving for variable 't'.

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

Add '1.09375' to each side of the equation.
-1.09375 + 1.09375 + t = 0.443045216 + 1.09375

Combine like terms: -1.09375 + 1.09375 = 0.00000
0.00000 + t = 0.443045216 + 1.09375
t = 0.443045216 + 1.09375

Combine like terms: 0.443045216 + 1.09375 = 1.536795216
t = 1.536795216

Simplifying
t = 1.536795216

Subproblem 2
t + -1.09375 = -0.443045216

Simplifying
t + -1.09375 = -0.443045216

Reorder the terms:
-1.09375 + t = -0.443045216

Solving
-1.09375 + t = -0.443045216

Solving for variable 't'.

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

Add '1.09375' to each side of the equation.
-1.09375 + 1.09375 + t = -0.443045216 + 1.09375

Combine like terms: -1.09375 + 1.09375 = 0.00000
0.00000 + t = -0.443045216 + 1.09375
t = -0.443045216 + 1.09375

Combine like terms: -0.443045216 + 1.09375 = 0.650704784
t = 0.650704784

Simplifying
t = 0.650704784

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.536795216, 0.650704784}