0=35-5t-5t^2

Solution for 0=35-5t-5t^2 equation:

Simplifying
0 = 35 + -5t + -5t2

Solving
0 = 35 + -5t + -5t2

Solving for variable 't'.

Combine like terms: 0 + -35 = -35
-35 + 5t + 5t2 = 35 + -5t + -5t2 + -35 + 5t + 5t2

Reorder the terms:
-35 + 5t + 5t2 = 35 + -35 + -5t + 5t + -5t2 + 5t2

Combine like terms: 35 + -35 = 0
-35 + 5t + 5t2 = 0 + -5t + 5t + -5t2 + 5t2
-35 + 5t + 5t2 = -5t + 5t + -5t2 + 5t2

Combine like terms: -5t + 5t = 0
-35 + 5t + 5t2 = 0 + -5t2 + 5t2
-35 + 5t + 5t2 = -5t2 + 5t2

Combine like terms: -5t2 + 5t2 = 0
-35 + 5t + 5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-7 + t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-7 + t + t2)' equal to zero and attempt to solve:

Simplifying
-7 + t + t2 = 0

Solving
-7 + t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + t + 7 + t2 = 0 + 7

Reorder the terms:
-7 + 7 + t + t2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + t + t2 = 0 + 7
t + t2 = 0 + 7

Combine like terms: 0 + 7 = 7
t + t2 = 7

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t + 0.25 + t2 = 7 + 0.25

Reorder the terms:
0.25 + t + t2 = 7 + 0.25

Combine like terms: 7 + 0.25 = 7.25
0.25 + t + t2 = 7.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(t + 0.5) equal to 2.692582404 and -2.692582404.

Subproblem 1
t + 0.5 = 2.692582404

Simplifying
t + 0.5 = 2.692582404

Reorder the terms:
0.5 + t = 2.692582404

Solving
0.5 + t = 2.692582404

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = 2.692582404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 2.692582404 + -0.5
t = 2.692582404 + -0.5

Combine like terms: 2.692582404 + -0.5 = 2.192582404
t = 2.192582404

Simplifying
t = 2.192582404

Subproblem 2
t + 0.5 = -2.692582404

Simplifying
t + 0.5 = -2.692582404

Reorder the terms:
0.5 + t = -2.692582404

Solving
0.5 + t = -2.692582404

Solving for variable 't'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + t = -2.692582404 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -2.692582404 + -0.5
t = -2.692582404 + -0.5

Combine like terms: -2.692582404 + -0.5 = -3.192582404
t = -3.192582404

Simplifying
t = -3.192582404

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.192582404, -3.192582404}
Solution
t = {2.192582404, -3.192582404}