-16t^2+150t+50=0

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Solution for -16t^2+150t+50=0 equation: 


Simplifying
-16t2 + 150t + 50 = 0

Reorder the terms:
50 + 150t + -16t2 = 0

Solving
50 + 150t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 75t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 75t + -8t2)' equal to zero and attempt to solve:

Simplifying
25 + 75t + -8t2 = 0

Solving
25 + 75t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-3.125 + -9.375t + t2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -9.375t + 3.125 + t2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -9.375t + t2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -9.375t + t2 = 0 + 3.125
-9.375t + t2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-9.375t + t2 = 3.125

The t term is -9.375t.  Take half its coefficient (-4.6875).
Square it (21.97265625) and add it to both sides.

Add '21.97265625' to each side of the equation.
-9.375t + 21.97265625 + t2 = 3.125 + 21.97265625

Reorder the terms:
21.97265625 + -9.375t + t2 = 3.125 + 21.97265625

Combine like terms: 3.125 + 21.97265625 = 25.09765625
21.97265625 + -9.375t + t2 = 25.09765625

Factor a perfect square on the left side:
(t + -4.6875)(t + -4.6875) = 25.09765625

Calculate the square root of the right side: 5.009756107

Break this problem into two subproblems by setting 
(t + -4.6875) equal to 5.009756107 and -5.009756107.


Subproblem 1
t + -4.6875 = 5.009756107

Simplifying
t + -4.6875 = 5.009756107

Reorder the terms:
-4.6875 + t = 5.009756107

Solving
-4.6875 + t = 5.009756107

Solving for variable 't'.

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

Add '4.6875' to each side of the equation.
-4.6875 + 4.6875 + t = 5.009756107 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + t = 5.009756107 + 4.6875
t = 5.009756107 + 4.6875

Combine like terms: 5.009756107 + 4.6875 = 9.697256107
t = 9.697256107

Simplifying
t = 9.697256107


Subproblem 2
t + -4.6875 = -5.009756107

Simplifying
t + -4.6875 = -5.009756107

Reorder the terms:
-4.6875 + t = -5.009756107

Solving
-4.6875 + t = -5.009756107

Solving for variable 't'.

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

Add '4.6875' to each side of the equation.
-4.6875 + 4.6875 + t = -5.009756107 + 4.6875

Combine like terms: -4.6875 + 4.6875 = 0.0000
0.0000 + t = -5.009756107 + 4.6875
t = -5.009756107 + 4.6875

Combine like terms: -5.009756107 + 4.6875 = -0.322256107
t = -0.322256107

Simplifying
t = -0.322256107


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.697256107, -0.322256107}
Solution
t = {9.697256107, -0.322256107}

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