50t^2+100t-60=100

Solution for 50t^2+100t-60=100 equation:

Simplifying
50t2 + 100t + -60 = 100

Reorder the terms:
-60 + 100t + 50t2 = 100

Solving
-60 + 100t + 50t2 = 100

Solving for variable 't'.

Reorder the terms:
-60 + -100 + 100t + 50t2 = 100 + -100

Combine like terms: -60 + -100 = -160
-160 + 100t + 50t2 = 100 + -100

Combine like terms: 100 + -100 = 0
-160 + 100t + 50t2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-16 + 10t + 5t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-16 + 10t + 5t2)' equal to zero and attempt to solve:

Simplifying
-16 + 10t + 5t2 = 0

Solving
-16 + 10t + 5t2 = 0

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

Divide each side by '5'.
-3.2 + 2t + t2 = 0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + 2t + 3.2 + t2 = 0 + 3.2

Reorder the terms:
-3.2 + 3.2 + 2t + t2 = 0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + 2t + t2 = 0 + 3.2
2t + t2 = 0 + 3.2

Combine like terms: 0 + 3.2 = 3.2
2t + t2 = 3.2

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 = 3.2 + 1

Reorder the terms:
1 + 2t + t2 = 3.2 + 1

Combine like terms: 3.2 + 1 = 4.2
1 + 2t + t2 = 4.2

Factor a perfect square on the left side:
(t + 1)(t + 1) = 4.2

Calculate the square root of the right side: 2.049390153

Break this problem into two subproblems by setting 
(t + 1) equal to 2.049390153 and -2.049390153.

Subproblem 1
t + 1 = 2.049390153

Simplifying
t + 1 = 2.049390153

Reorder the terms:
1 + t = 2.049390153

Solving
1 + t = 2.049390153

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 = 2.049390153 + -1

Combine like terms: 1 + -1 = 0
0 + t = 2.049390153 + -1
t = 2.049390153 + -1

Combine like terms: 2.049390153 + -1 = 1.049390153
t = 1.049390153

Simplifying
t = 1.049390153

Subproblem 2
t + 1 = -2.049390153

Simplifying
t + 1 = -2.049390153

Reorder the terms:
1 + t = -2.049390153

Solving
1 + t = -2.049390153

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 = -2.049390153 + -1

Combine like terms: 1 + -1 = 0
0 + t = -2.049390153 + -1
t = -2.049390153 + -1

Combine like terms: -2.049390153 + -1 = -3.049390153
t = -3.049390153

Simplifying
t = -3.049390153

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.049390153, -3.049390153}
Solution
t = {1.049390153, -3.049390153}