-16t^2+30t+50=0

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Solution for -16t^2+30t+50=0 equation: 


Simplifying
-16t2 + 30t + 50 = 0

Reorder the terms:
50 + 30t + -16t2 = 0

Solving
50 + 30t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 15t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 15t + -8t2)' equal to zero and attempt to solve:

Simplifying
25 + 15t + -8t2 = 0

Solving
25 + 15t + -8t2 = 0

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

Divide each side by '-8'.
-3.125 + -1.875t + t2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -1.875t + 3.125 + t2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -1.875t + t2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -1.875t + t2 = 0 + 3.125
-1.875t + t2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-1.875t + t2 = 3.125

The t term is -1.875t.  Take half its coefficient (-0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
-1.875t + 0.87890625 + t2 = 3.125 + 0.87890625

Reorder the terms:
0.87890625 + -1.875t + t2 = 3.125 + 0.87890625

Combine like terms: 3.125 + 0.87890625 = 4.00390625
0.87890625 + -1.875t + t2 = 4.00390625

Factor a perfect square on the left side:
(t + -0.9375)(t + -0.9375) = 4.00390625

Calculate the square root of the right side: 2.000976324

Break this problem into two subproblems by setting 
(t + -0.9375) equal to 2.000976324 and -2.000976324.


Subproblem 1
t + -0.9375 = 2.000976324

Simplifying
t + -0.9375 = 2.000976324

Reorder the terms:
-0.9375 + t = 2.000976324

Solving
-0.9375 + t = 2.000976324

Solving for variable 't'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + t = 2.000976324 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + t = 2.000976324 + 0.9375
t = 2.000976324 + 0.9375

Combine like terms: 2.000976324 + 0.9375 = 2.938476324
t = 2.938476324

Simplifying
t = 2.938476324


Subproblem 2
t + -0.9375 = -2.000976324

Simplifying
t + -0.9375 = -2.000976324

Reorder the terms:
-0.9375 + t = -2.000976324

Solving
-0.9375 + t = -2.000976324

Solving for variable 't'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + t = -2.000976324 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + t = -2.000976324 + 0.9375
t = -2.000976324 + 0.9375

Combine like terms: -2.000976324 + 0.9375 = -1.063476324
t = -1.063476324

Simplifying
t = -1.063476324


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.938476324, -1.063476324}
Solution
t = {2.938476324, -1.063476324}

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