-16t^2+30t+5=0

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Solution for -16t^2+30t+5=0 equation: 


Simplifying
-16t2 + 30t + 5 = 0

Reorder the terms:
5 + 30t + -16t2 = 0

Solving
5 + 30t + -16t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-0.3125 + -1.875t + t2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -1.875t + 0.3125 + t2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -1.875t + t2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -1.875t + t2 = 0 + 0.3125
-1.875t + t2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-1.875t + t2 = 0.3125

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 = 0.3125 + 0.87890625

Reorder the terms:
0.87890625 + -1.875t + t2 = 0.3125 + 0.87890625

Combine like terms: 0.3125 + 0.87890625 = 1.19140625
0.87890625 + -1.875t + t2 = 1.19140625

Factor a perfect square on the left side:
(t + -0.9375)(t + -0.9375) = 1.19140625

Calculate the square root of the right side: 1.091515575

Break this problem into two subproblems by setting 
(t + -0.9375) equal to 1.091515575 and -1.091515575.


Subproblem 1
t + -0.9375 = 1.091515575

Simplifying
t + -0.9375 = 1.091515575

Reorder the terms:
-0.9375 + t = 1.091515575

Solving
-0.9375 + t = 1.091515575

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 = 1.091515575 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + t = 1.091515575 + 0.9375
t = 1.091515575 + 0.9375

Combine like terms: 1.091515575 + 0.9375 = 2.029015575
t = 2.029015575

Simplifying
t = 2.029015575


Subproblem 2
t + -0.9375 = -1.091515575

Simplifying
t + -0.9375 = -1.091515575

Reorder the terms:
-0.9375 + t = -1.091515575

Solving
-0.9375 + t = -1.091515575

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 = -1.091515575 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + t = -1.091515575 + 0.9375
t = -1.091515575 + 0.9375

Combine like terms: -1.091515575 + 0.9375 = -0.154015575
t = -0.154015575

Simplifying
t = -0.154015575


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {2.029015575, -0.154015575}

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