50=35t+5t^2

Solution for 50=35t+5t^2 equation:

Simplifying
50 = 35t + 5t2

Solving
50 = 35t + 5t2

Solving for variable 't'.

Reorder the terms:
50 + -35t + -5t2 = 35t + -35t + 5t2 + -5t2

Combine like terms: 35t + -35t = 0
50 + -35t + -5t2 = 0 + 5t2 + -5t2
50 + -35t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
50 + -35t + -5t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(10 + -7t + -1t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(10 + -7t + -1t2)' equal to zero and attempt to solve:

Simplifying
10 + -7t + -1t2 = 0

Solving
10 + -7t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + 7t + t2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 7t + 10 + t2 = 0 + 10

Reorder the terms:
-10 + 10 + 7t + t2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + 7t + t2 = 0 + 10
7t + t2 = 0 + 10

Combine like terms: 0 + 10 = 10
7t + t2 = 10

The t term is 7t.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7t + 12.25 + t2 = 10 + 12.25

Reorder the terms:
12.25 + 7t + t2 = 10 + 12.25

Combine like terms: 10 + 12.25 = 22.25
12.25 + 7t + t2 = 22.25

Factor a perfect square on the left side:
(t + 3.5)(t + 3.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(t + 3.5) equal to 4.716990566 and -4.716990566.

Subproblem 1
t + 3.5 = 4.716990566

Simplifying
t + 3.5 = 4.716990566

Reorder the terms:
3.5 + t = 4.716990566

Solving
3.5 + t = 4.716990566

Solving for variable 't'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + t = 4.716990566 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = 4.716990566 + -3.5
t = 4.716990566 + -3.5

Combine like terms: 4.716990566 + -3.5 = 1.216990566
t = 1.216990566

Simplifying
t = 1.216990566

Subproblem 2
t + 3.5 = -4.716990566

Simplifying
t + 3.5 = -4.716990566

Reorder the terms:
3.5 + t = -4.716990566

Solving
3.5 + t = -4.716990566

Solving for variable 't'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + t = -4.716990566 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + t = -4.716990566 + -3.5
t = -4.716990566 + -3.5

Combine like terms: -4.716990566 + -3.5 = -8.216990566
t = -8.216990566

Simplifying
t = -8.216990566

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.216990566, -8.216990566}
Solution
t = {1.216990566, -8.216990566}