16t^2-120t-50=0

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Solution for 16t^2-120t-50=0 equation: 


Simplifying
16t2 + -120t + -50 = 0

Reorder the terms:
-50 + -120t + 16t2 = 0

Solving
-50 + -120t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-25 + -60t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-25 + -60t + 8t2)' equal to zero and attempt to solve:

Simplifying
-25 + -60t + 8t2 = 0

Solving
-25 + -60t + 8t2 = 0

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

Divide each side by '8'.
-3.125 + -7.5t + t2 = 0

Move the constant term to the right:

Add '3.125' to each side of the equation.
-3.125 + -7.5t + 3.125 + t2 = 0 + 3.125

Reorder the terms:
-3.125 + 3.125 + -7.5t + t2 = 0 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + -7.5t + t2 = 0 + 3.125
-7.5t + t2 = 0 + 3.125

Combine like terms: 0 + 3.125 = 3.125
-7.5t + t2 = 3.125

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 = 3.125 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = 3.125 + 14.0625

Combine like terms: 3.125 + 14.0625 = 17.1875
14.0625 + -7.5t + t2 = 17.1875

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 17.1875

Calculate the square root of the right side: 4.145780988

Break this problem into two subproblems by setting 
(t + -3.75) equal to 4.145780988 and -4.145780988.


Subproblem 1
t + -3.75 = 4.145780988

Simplifying
t + -3.75 = 4.145780988

Reorder the terms:
-3.75 + t = 4.145780988

Solving
-3.75 + t = 4.145780988

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 = 4.145780988 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 4.145780988 + 3.75
t = 4.145780988 + 3.75

Combine like terms: 4.145780988 + 3.75 = 7.895780988
t = 7.895780988

Simplifying
t = 7.895780988


Subproblem 2
t + -3.75 = -4.145780988

Simplifying
t + -3.75 = -4.145780988

Reorder the terms:
-3.75 + t = -4.145780988

Solving
-3.75 + t = -4.145780988

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 = -4.145780988 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -4.145780988 + 3.75
t = -4.145780988 + 3.75

Combine like terms: -4.145780988 + 3.75 = -0.395780988
t = -0.395780988

Simplifying
t = -0.395780988


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.895780988, -0.395780988}
Solution
t = {7.895780988, -0.395780988}

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