-16t^2+120t+2=0

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Solution for -16t^2+120t+2=0 equation: 


Simplifying
-16t2 + 120t + 2 = 0

Reorder the terms:
2 + 120t + -16t2 = 0

Solving
2 + 120t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 60t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + 60t + -8t2)' equal to zero and attempt to solve:

Simplifying
1 + 60t + -8t2 = 0

Solving
1 + 60t + -8t2 = 0

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

Divide each side by '-8'.
-0.125 + -7.5t + t2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -7.5t + 0.125 + t2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -7.5t + t2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -7.5t + t2 = 0 + 0.125
-7.5t + t2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-7.5t + t2 = 0.125

The t term is -7.5t.  Take half its coefficient (-3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
-7.5t + 14.0625 + t2 = 0.125 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = 0.125 + 14.0625

Combine like terms: 0.125 + 14.0625 = 14.1875
14.0625 + -7.5t + t2 = 14.1875

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 14.1875

Calculate the square root of the right side: 3.766629793

Break this problem into two subproblems by setting 
(t + -3.75) equal to 3.766629793 and -3.766629793.


Subproblem 1
t + -3.75 = 3.766629793

Simplifying
t + -3.75 = 3.766629793

Reorder the terms:
-3.75 + t = 3.766629793

Solving
-3.75 + t = 3.766629793

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = 3.766629793 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 3.766629793 + 3.75
t = 3.766629793 + 3.75

Combine like terms: 3.766629793 + 3.75 = 7.516629793
t = 7.516629793

Simplifying
t = 7.516629793


Subproblem 2
t + -3.75 = -3.766629793

Simplifying
t + -3.75 = -3.766629793

Reorder the terms:
-3.75 + t = -3.766629793

Solving
-3.75 + t = -3.766629793

Solving for variable 't'.

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

Add '3.75' to each side of the equation.
-3.75 + 3.75 + t = -3.766629793 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -3.766629793 + 3.75
t = -3.766629793 + 3.75

Combine like terms: -3.766629793 + 3.75 = -0.016629793
t = -0.016629793

Simplifying
t = -0.016629793


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.516629793, -0.016629793}
Solution
t = {7.516629793, -0.016629793}

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