50=5t+5t^2

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

Simplifying
50 = 5t + 5t2

Solving
50 = 5t + 5t2

Solving for variable 't'.

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

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

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

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

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

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

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

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

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

Move the constant term to the right:

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

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

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

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

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.
 + 0.25 + t2 = 10 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + t2 = 10 + 0.25

Combine like terms: 10 + 0.25 = 10.25
1.25 + t2 = 10.25

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 10.25

Calculate the square root of the right side: 3.201562119

Break this problem into two subproblems by setting 
(t + 0.5) equal to 3.201562119 and -3.201562119.

Subproblem 1
t + 0.5 = 3.201562119

Simplifying
t + 0.5 = 3.201562119

Reorder the terms:
0.5 + t = 3.201562119

Solving
0.5 + t = 3.201562119

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 = 3.201562119 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = 3.201562119 + -0.5
t = 3.201562119 + -0.5

Combine like terms: 3.201562119 + -0.5 = 2.701562119
t = 2.701562119

Simplifying
t = 2.701562119

Subproblem 2
t + 0.5 = -3.201562119

Simplifying
t + 0.5 = -3.201562119

Reorder the terms:
0.5 + t = -3.201562119

Solving
0.5 + t = -3.201562119

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 = -3.201562119 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + t = -3.201562119 + -0.5
t = -3.201562119 + -0.5

Combine like terms: -3.201562119 + -0.5 = -3.701562119
t = -3.701562119

Simplifying
t = -3.701562119

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.701562119, -3.701562119}
Solution
t = {2.701562119, -3.701562119}