16.8=17.6t-0.8t^2

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Solution for 16.8=17.6t-0.8t^2 equation: 


Simplifying
16.8 = 17.6t + -0.8t2

Solving
16.8 = 17.6t + -0.8t2

Solving for variable 't'.

Reorder the terms:
16.8 + -17.6t + 0.8t2 = 17.6t + -17.6t + -0.8t2 + 0.8t2

Combine like terms: 17.6t + -17.6t = 0.0
16.8 + -17.6t + 0.8t2 = 0.0 + -0.8t2 + 0.8t2
16.8 + -17.6t + 0.8t2 = -0.8t2 + 0.8t2

Combine like terms: -0.8t2 + 0.8t2 = 0.0
16.8 + -17.6t + 0.8t2 = 0.0

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

Divide each side by '0.8'.
21 + -22t + t2 = 0

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -22t + -21 + t2 = 0 + -21

Reorder the terms:
21 + -21 + -22t + t2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -22t + t2 = 0 + -21
-22t + t2 = 0 + -21

Combine like terms: 0 + -21 = -21
-22t + t2 = -21

The t term is -22t.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22t + 121 + t2 = -21 + 121

Reorder the terms:
121 + -22t + t2 = -21 + 121

Combine like terms: -21 + 121 = 100
121 + -22t + t2 = 100

Factor a perfect square on the left side:
(t + -11)(t + -11) = 100

Calculate the square root of the right side: 10

Break this problem into two subproblems by setting 
(t + -11) equal to 10 and -10.


Subproblem 1
t + -11 = 10

Simplifying
t + -11 = 10

Reorder the terms:
-11 + t = 10

Solving
-11 + t = 10

Solving for variable 't'.

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

Add '11' to each side of the equation.
-11 + 11 + t = 10 + 11

Combine like terms: -11 + 11 = 0
0 + t = 10 + 11
t = 10 + 11

Combine like terms: 10 + 11 = 21
t = 21

Simplifying
t = 21


Subproblem 2
t + -11 = -10

Simplifying
t + -11 = -10

Reorder the terms:
-11 + t = -10

Solving
-11 + t = -10

Solving for variable 't'.

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

Add '11' to each side of the equation.
-11 + 11 + t = -10 + 11

Combine like terms: -11 + 11 = 0
0 + t = -10 + 11
t = -10 + 11

Combine like terms: -10 + 11 = 1
t = 1

Simplifying
t = 1


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {21, 1}

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