0=10+160t-16t^2

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Solution for 0=10+160t-16t^2 equation: 


Simplifying
0 = 10 + 160t + -16t2

Solving
0 = 10 + 160t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -10 = -10
-10 + -160t + 16t2 = 10 + 160t + -16t2 + -10 + -160t + 16t2

Reorder the terms:
-10 + -160t + 16t2 = 10 + -10 + 160t + -160t + -16t2 + 16t2

Combine like terms: 10 + -10 = 0
-10 + -160t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2
-10 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2

Combine like terms: 160t + -160t = 0
-10 + -160t + 16t2 = 0 + -16t2 + 16t2
-10 + -160t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-10 + -160t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -80t + 8t2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + -80t + 8t2)' equal to zero and attempt to solve:

Simplifying
-5 + -80t + 8t2 = 0

Solving
-5 + -80t + 8t2 = 0

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

Divide each side by '8'.
-0.625 + -10t + t2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + -10t + 0.625 + t2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + -10t + t2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + -10t + t2 = 0 + 0.625
-10t + t2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
-10t + t2 = 0.625

The t term is -10t.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10t + 25 + t2 = 0.625 + 25

Reorder the terms:
25 + -10t + t2 = 0.625 + 25

Combine like terms: 0.625 + 25 = 25.625
25 + -10t + t2 = 25.625

Factor a perfect square on the left side:
(t + -5)(t + -5) = 25.625

Calculate the square root of the right side: 5.062114183

Break this problem into two subproblems by setting 
(t + -5) equal to 5.062114183 and -5.062114183.


Subproblem 1
t + -5 = 5.062114183

Simplifying
t + -5 = 5.062114183

Reorder the terms:
-5 + t = 5.062114183

Solving
-5 + t = 5.062114183

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = 5.062114183 + 5

Combine like terms: -5 + 5 = 0
0 + t = 5.062114183 + 5
t = 5.062114183 + 5

Combine like terms: 5.062114183 + 5 = 10.062114183
t = 10.062114183

Simplifying
t = 10.062114183


Subproblem 2
t + -5 = -5.062114183

Simplifying
t + -5 = -5.062114183

Reorder the terms:
-5 + t = -5.062114183

Solving
-5 + t = -5.062114183

Solving for variable 't'.

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

Add '5' to each side of the equation.
-5 + 5 + t = -5.062114183 + 5

Combine like terms: -5 + 5 = 0
0 + t = -5.062114183 + 5
t = -5.062114183 + 5

Combine like terms: -5.062114183 + 5 = -0.062114183
t = -0.062114183

Simplifying
t = -0.062114183


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10.062114183, -0.062114183}
Solution
t = {10.062114183, -0.062114183}

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