16t^2-96t+50=0

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Solution for 16t^2-96t+50=0 equation: 


Simplifying
16t2 + -96t + 50 = 0

Reorder the terms:
50 + -96t + 16t2 = 0

Solving
50 + -96t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -48t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + -48t + 8t2)' equal to zero and attempt to solve:

Simplifying
25 + -48t + 8t2 = 0

Solving
25 + -48t + 8t2 = 0

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

Divide each side by '8'.
3.125 + -6t + t2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + -6t + -3.125 + t2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + -6t + t2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + -6t + t2 = 0 + -3.125
-6t + t2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
-6t + t2 = -3.125

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = -3.125 + 9

Reorder the terms:
9 + -6t + t2 = -3.125 + 9

Combine like terms: -3.125 + 9 = 5.875
9 + -6t + t2 = 5.875

Factor a perfect square on the left side:
(t + -3)(t + -3) = 5.875

Calculate the square root of the right side: 2.423839929

Break this problem into two subproblems by setting 
(t + -3) equal to 2.423839929 and -2.423839929.


Subproblem 1
t + -3 = 2.423839929

Simplifying
t + -3 = 2.423839929

Reorder the terms:
-3 + t = 2.423839929

Solving
-3 + t = 2.423839929

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 2.423839929 + 3

Combine like terms: -3 + 3 = 0
0 + t = 2.423839929 + 3
t = 2.423839929 + 3

Combine like terms: 2.423839929 + 3 = 5.423839929
t = 5.423839929

Simplifying
t = 5.423839929


Subproblem 2
t + -3 = -2.423839929

Simplifying
t + -3 = -2.423839929

Reorder the terms:
-3 + t = -2.423839929

Solving
-3 + t = -2.423839929

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -2.423839929 + 3

Combine like terms: -3 + 3 = 0
0 + t = -2.423839929 + 3
t = -2.423839929 + 3

Combine like terms: -2.423839929 + 3 = 0.576160071
t = 0.576160071

Simplifying
t = 0.576160071


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.423839929, 0.576160071}
Solution
t = {5.423839929, 0.576160071}

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