Answer:
about 11.856 time units
Explanation:
We have to assume the equation has something to do with the path of the ball relative to the ground. Perhaps it represents height, with t representing time. The height (h) will be zero for the values of t that satisfy ...
0 = -t^2 +10t +22
Using the quadratic formula, we can find the values of t that satisfy this equation:
t = (-10 ±√(10² -4(-1)(22)))/(2(-1)) = (-10 ±√188)/-2 = 5±√47
The value of h is zero for t ≈ 11.856.
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About the quadratic formula
The quadratic formula tells you the solution to ...
ax^2 +bx +c = 0
is given by ...
x = (-b ±√(b^2 -4ac))/(2a)
Matching this form to the given equation, we see a=-1, b=10, c=22. The variable used in the given equation is t, instead of x.