384=-16t^2+164t

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Solution for 384=-16t^2+164t equation: 


Simplifying
384 = -16t2 + 164t

Reorder the terms:
384 = 164t + -16t2

Solving
384 = 164t + -16t2

Solving for variable 't'.

Reorder the terms:
384 + -164t + 16t2 = 164t + -164t + -16t2 + 16t2

Combine like terms: 164t + -164t = 0
384 + -164t + 16t2 = 0 + -16t2 + 16t2
384 + -164t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
384 + -164t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(96 + -41t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(96 + -41t + 4t2)' equal to zero and attempt to solve:

Simplifying
96 + -41t + 4t2 = 0

Solving
96 + -41t + 4t2 = 0

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

Divide each side by '4'.
24 + -10.25t + t2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -10.25t + -24 + t2 = 0 + -24

Reorder the terms:
24 + -24 + -10.25t + t2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -10.25t + t2 = 0 + -24
-10.25t + t2 = 0 + -24

Combine like terms: 0 + -24 = -24
-10.25t + t2 = -24

The t term is -10.25t.  Take half its coefficient (-5.125).
Square it (26.265625) and add it to both sides.

Add '26.265625' to each side of the equation.
-10.25t + 26.265625 + t2 = -24 + 26.265625

Reorder the terms:
26.265625 + -10.25t + t2 = -24 + 26.265625

Combine like terms: -24 + 26.265625 = 2.265625
26.265625 + -10.25t + t2 = 2.265625

Factor a perfect square on the left side:
(t + -5.125)(t + -5.125) = 2.265625

Calculate the square root of the right side: 1.505199322

Break this problem into two subproblems by setting 
(t + -5.125) equal to 1.505199322 and -1.505199322.


Subproblem 1
t + -5.125 = 1.505199322

Simplifying
t + -5.125 = 1.505199322

Reorder the terms:
-5.125 + t = 1.505199322

Solving
-5.125 + t = 1.505199322

Solving for variable 't'.

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

Add '5.125' to each side of the equation.
-5.125 + 5.125 + t = 1.505199322 + 5.125

Combine like terms: -5.125 + 5.125 = 0.000
0.000 + t = 1.505199322 + 5.125
t = 1.505199322 + 5.125

Combine like terms: 1.505199322 + 5.125 = 6.630199322
t = 6.630199322

Simplifying
t = 6.630199322


Subproblem 2
t + -5.125 = -1.505199322

Simplifying
t + -5.125 = -1.505199322

Reorder the terms:
-5.125 + t = -1.505199322

Solving
-5.125 + t = -1.505199322

Solving for variable 't'.

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

Add '5.125' to each side of the equation.
-5.125 + 5.125 + t = -1.505199322 + 5.125

Combine like terms: -5.125 + 5.125 = 0.000
0.000 + t = -1.505199322 + 5.125
t = -1.505199322 + 5.125

Combine like terms: -1.505199322 + 5.125 = 3.619800678
t = 3.619800678

Simplifying
t = 3.619800678


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.630199322, 3.619800678}
Solution
t = {6.630199322, 3.619800678}

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