0=-16t^2+32t+100

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Solution for 0=-16t^2+32t+100 equation: 


Simplifying
0 = -16t2 + 32t + 100

Reorder the terms:
0 = 100 + 32t + -16t2

Solving
0 = 100 + 32t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -100 = -100
-100 + -32t + 16t2 = 100 + 32t + -16t2 + -100 + -32t + 16t2

Reorder the terms:
-100 + -32t + 16t2 = 100 + -100 + 32t + -32t + -16t2 + 16t2

Combine like terms: 100 + -100 = 0
-100 + -32t + 16t2 = 0 + 32t + -32t + -16t2 + 16t2
-100 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-100 + -32t + 16t2 = 0 + -16t2 + 16t2
-100 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-100 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + -8t + 4t2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-25 + -8t + 4t2)' equal to zero and attempt to solve:

Simplifying
-25 + -8t + 4t2 = 0

Solving
-25 + -8t + 4t2 = 0

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

Divide each side by '4'.
-6.25 + -2t + t2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -2t + 6.25 + t2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -2t + t2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -2t + t2 = 0 + 6.25
-2t + t2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-2t + t2 = 6.25

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 6.25 + 1

Reorder the terms:
1 + -2t + t2 = 6.25 + 1

Combine like terms: 6.25 + 1 = 7.25
1 + -2t + t2 = 7.25

Factor a perfect square on the left side:
(t + -1)(t + -1) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(t + -1) equal to 2.692582404 and -2.692582404.


Subproblem 1
t + -1 = 2.692582404

Simplifying
t + -1 = 2.692582404

Reorder the terms:
-1 + t = 2.692582404

Solving
-1 + t = 2.692582404

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 2.692582404 + 1

Combine like terms: -1 + 1 = 0
0 + t = 2.692582404 + 1
t = 2.692582404 + 1

Combine like terms: 2.692582404 + 1 = 3.692582404
t = 3.692582404

Simplifying
t = 3.692582404


Subproblem 2
t + -1 = -2.692582404

Simplifying
t + -1 = -2.692582404

Reorder the terms:
-1 + t = -2.692582404

Solving
-1 + t = -2.692582404

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -2.692582404 + 1

Combine like terms: -1 + 1 = 0
0 + t = -2.692582404 + 1
t = -2.692582404 + 1

Combine like terms: -2.692582404 + 1 = -1.692582404
t = -1.692582404

Simplifying
t = -1.692582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.692582404, -1.692582404}
Solution
t = {3.692582404, -1.692582404}

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