-16t^2+120t+10=0

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Solution for -16t^2+120t+10=0 equation: 


Simplifying
-16t2 + 120t + 10 = 0

Reorder the terms:
10 + 120t + -16t2 = 0

Solving
10 + 120t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 60t + -8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 60t + -8t2)' equal to zero and attempt to solve:

Simplifying
5 + 60t + -8t2 = 0

Solving
5 + 60t + -8t2 = 0

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

Divide each side by '-8'.
-0.625 + -7.5t + t2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -7.5t + 0.625 + t2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -7.5t + t2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -7.5t + t2 = 0 + 0.625
-7.5t + t2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-7.5t + t2 = 0.625

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 = 0.625 + 14.0625

Reorder the terms:
14.0625 + -7.5t + t2 = 0.625 + 14.0625

Combine like terms: 0.625 + 14.0625 = 14.6875
14.0625 + -7.5t + t2 = 14.6875

Factor a perfect square on the left side:
(t + -3.75)(t + -3.75) = 14.6875

Calculate the square root of the right side: 3.832427429

Break this problem into two subproblems by setting 
(t + -3.75) equal to 3.832427429 and -3.832427429.


Subproblem 1
t + -3.75 = 3.832427429

Simplifying
t + -3.75 = 3.832427429

Reorder the terms:
-3.75 + t = 3.832427429

Solving
-3.75 + t = 3.832427429

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 = 3.832427429 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = 3.832427429 + 3.75
t = 3.832427429 + 3.75

Combine like terms: 3.832427429 + 3.75 = 7.582427429
t = 7.582427429

Simplifying
t = 7.582427429


Subproblem 2
t + -3.75 = -3.832427429

Simplifying
t + -3.75 = -3.832427429

Reorder the terms:
-3.75 + t = -3.832427429

Solving
-3.75 + t = -3.832427429

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 = -3.832427429 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + t = -3.832427429 + 3.75
t = -3.832427429 + 3.75

Combine like terms: -3.832427429 + 3.75 = -0.082427429
t = -0.082427429

Simplifying
t = -0.082427429


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {7.582427429, -0.082427429}
Solution
t = {7.582427429, -0.082427429}

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