-16t^2+320t=1538

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Solution for -16t^2+320t=1538 equation: 


Simplifying
-16t2 + 320t = 1538

Reorder the terms:
320t + -16t2 = 1538

Solving
320t + -16t2 = 1538

Solving for variable 't'.

Reorder the terms:
-1538 + 320t + -16t2 = 1538 + -1538

Combine like terms: 1538 + -1538 = 0
-1538 + 320t + -16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-769 + 160t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-769 + 160t + -8t2)' equal to zero and attempt to solve:

Simplifying
-769 + 160t + -8t2 = 0

Solving
-769 + 160t + -8t2 = 0

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

Divide each side by '-8'.
96.125 + -20t + t2 = 0

Move the constant term to the right:

Add '-96.125' to each side of the equation.
96.125 + -20t + -96.125 + t2 = 0 + -96.125

Reorder the terms:
96.125 + -96.125 + -20t + t2 = 0 + -96.125

Combine like terms: 96.125 + -96.125 = 0.000
0.000 + -20t + t2 = 0 + -96.125
-20t + t2 = 0 + -96.125

Combine like terms: 0 + -96.125 = -96.125
-20t + t2 = -96.125

The t term is -20t.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20t + 100 + t2 = -96.125 + 100

Reorder the terms:
100 + -20t + t2 = -96.125 + 100

Combine like terms: -96.125 + 100 = 3.875
100 + -20t + t2 = 3.875

Factor a perfect square on the left side:
(t + -10)(t + -10) = 3.875

Calculate the square root of the right side: 1.968501969

Break this problem into two subproblems by setting 
(t + -10) equal to 1.968501969 and -1.968501969.


Subproblem 1
t + -10 = 1.968501969

Simplifying
t + -10 = 1.968501969

Reorder the terms:
-10 + t = 1.968501969

Solving
-10 + t = 1.968501969

Solving for variable 't'.

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

Add '10' to each side of the equation.
-10 + 10 + t = 1.968501969 + 10

Combine like terms: -10 + 10 = 0
0 + t = 1.968501969 + 10
t = 1.968501969 + 10

Combine like terms: 1.968501969 + 10 = 11.968501969
t = 11.968501969

Simplifying
t = 11.968501969


Subproblem 2
t + -10 = -1.968501969

Simplifying
t + -10 = -1.968501969

Reorder the terms:
-10 + t = -1.968501969

Solving
-10 + t = -1.968501969

Solving for variable 't'.

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

Add '10' to each side of the equation.
-10 + 10 + t = -1.968501969 + 10

Combine like terms: -10 + 10 = 0
0 + t = -1.968501969 + 10
t = -1.968501969 + 10

Combine like terms: -1.968501969 + 10 = 8.031498031
t = 8.031498031

Simplifying
t = 8.031498031


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {11.968501969, 8.031498031}
Solution
t = {11.968501969, 8.031498031}

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