-16t^2+70t+4=0

Solution for -16t^2+70t+4=0 equation:

Simplifying
-16t2 + 70t + 4 = 0

Reorder the terms:
4 + 70t + -16t2 = 0

Solving
4 + 70t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + 35t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + 35t + -8t2)' equal to zero and attempt to solve:

Simplifying
2 + 35t + -8t2 = 0

Solving
2 + 35t + -8t2 = 0

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

Divide each side by '-8'.
-0.25 + -4.375t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -4.375t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -4.375t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -4.375t + t2 = 0 + 0.25
-4.375t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-4.375t + t2 = 0.25

The t term is -4.375t.  Take half its coefficient (-2.1875).
Square it (4.78515625) and add it to both sides.

Add '4.78515625' to each side of the equation.
-4.375t + 4.78515625 + t2 = 0.25 + 4.78515625

Reorder the terms:
4.78515625 + -4.375t + t2 = 0.25 + 4.78515625

Combine like terms: 0.25 + 4.78515625 = 5.03515625
4.78515625 + -4.375t + t2 = 5.03515625

Factor a perfect square on the left side:
(t + -2.1875)(t + -2.1875) = 5.03515625

Calculate the square root of the right side: 2.243915384

Break this problem into two subproblems by setting 
(t + -2.1875) equal to 2.243915384 and -2.243915384.

Subproblem 1
t + -2.1875 = 2.243915384

Simplifying
t + -2.1875 = 2.243915384

Reorder the terms:
-2.1875 + t = 2.243915384

Solving
-2.1875 + t = 2.243915384

Solving for variable 't'.

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

Add '2.1875' to each side of the equation.
-2.1875 + 2.1875 + t = 2.243915384 + 2.1875

Combine like terms: -2.1875 + 2.1875 = 0.0000
0.0000 + t = 2.243915384 + 2.1875
t = 2.243915384 + 2.1875

Combine like terms: 2.243915384 + 2.1875 = 4.431415384
t = 4.431415384

Simplifying
t = 4.431415384

Subproblem 2
t + -2.1875 = -2.243915384

Simplifying
t + -2.1875 = -2.243915384

Reorder the terms:
-2.1875 + t = -2.243915384

Solving
-2.1875 + t = -2.243915384

Solving for variable 't'.

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

Add '2.1875' to each side of the equation.
-2.1875 + 2.1875 + t = -2.243915384 + 2.1875

Combine like terms: -2.1875 + 2.1875 = 0.0000
0.0000 + t = -2.243915384 + 2.1875
t = -2.243915384 + 2.1875

Combine like terms: -2.243915384 + 2.1875 = -0.056415384
t = -0.056415384

Simplifying
t = -0.056415384

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.431415384, -0.056415384}
Solution
t = {4.431415384, -0.056415384}