-16t^2+160t+4=0

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Solution for -16t^2+160t+4=0 equation: 


Simplifying
-16t2 + 160t + 4 = 0

Reorder the terms:
4 + 160t + -16t2 = 0

Solving
4 + 160t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 40t + -4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + 40t + -4t2)' equal to zero and attempt to solve:

Simplifying
1 + 40t + -4t2 = 0

Solving
1 + 40t + -4t2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -10t + t2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -10t + 0.25 + t2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -10t + t2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -10t + t2 = 0 + 0.25
-10t + t2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-10t + t2 = 0.25

The t term is -10t.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10t + 25 + t2 = 0.25 + 25

Reorder the terms:
25 + -10t + t2 = 0.25 + 25

Combine like terms: 0.25 + 25 = 25.25
25 + -10t + t2 = 25.25

Factor a perfect square on the left side:
(t + -5)(t + -5) = 25.25

Calculate the square root of the right side: 5.024937811

Break this problem into two subproblems by setting 
(t + -5) equal to 5.024937811 and -5.024937811.


Subproblem 1
t + -5 = 5.024937811

Simplifying
t + -5 = 5.024937811

Reorder the terms:
-5 + t = 5.024937811

Solving
-5 + t = 5.024937811

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = 5.024937811 + 5

Combine like terms: -5 + 5 = 0
0 + t = 5.024937811 + 5
t = 5.024937811 + 5

Combine like terms: 5.024937811 + 5 = 10.024937811
t = 10.024937811

Simplifying
t = 10.024937811


Subproblem 2
t + -5 = -5.024937811

Simplifying
t + -5 = -5.024937811

Reorder the terms:
-5 + t = -5.024937811

Solving
-5 + t = -5.024937811

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = -5.024937811 + 5

Combine like terms: -5 + 5 = 0
0 + t = -5.024937811 + 5
t = -5.024937811 + 5

Combine like terms: -5.024937811 + 5 = -0.024937811
t = -0.024937811

Simplifying
t = -0.024937811


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.024937811, -0.024937811}
Solution
t = {10.024937811, -0.024937811}

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