5t^2-10t-50=0

Solution for 5t^2-10t-50=0 equation:

Simplifying
5t2 + -10t + -50 = 0

Reorder the terms:
-50 + -10t + 5t2 = 0

Solving
-50 + -10t + 5t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + -2t + t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-10 + -2t + t2)' equal to zero and attempt to solve:

Simplifying
-10 + -2t + t2 = 0

Solving
-10 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2t + 10 + t2 = 0 + 10

Reorder the terms:
-10 + 10 + -2t + t2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2t + t2 = 0 + 10
-2t + t2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2t + t2 = 10

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 10 + 1

Reorder the terms:
1 + -2t + t2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + -2t + t2 = 11

Factor a perfect square on the left side:
(t + -1)(t + -1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(t + -1) equal to 3.31662479 and -3.31662479.

Subproblem 1
t + -1 = 3.31662479

Simplifying
t + -1 = 3.31662479

Reorder the terms:
-1 + t = 3.31662479

Solving
-1 + t = 3.31662479

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + t = 3.31662479 + 1
t = 3.31662479 + 1

Combine like terms: 3.31662479 + 1 = 4.31662479
t = 4.31662479

Simplifying
t = 4.31662479

Subproblem 2
t + -1 = -3.31662479

Simplifying
t + -1 = -3.31662479

Reorder the terms:
-1 + t = -3.31662479

Solving
-1 + t = -3.31662479

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + t = -3.31662479 + 1
t = -3.31662479 + 1

Combine like terms: -3.31662479 + 1 = -2.31662479
t = -2.31662479

Simplifying
t = -2.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.31662479, -2.31662479}
Solution
t = {4.31662479, -2.31662479}