# Solve for t -16t^2-22t+100=h

-16t2-22t+100=h
Move h to the left side of the equation by subtracting it from both sides.
-16t2-22t+100-h=0
Use the quadratic formula to find the solutions.
-b±b2-4(ac)2a
Substitute the values a=-16, b=-22, and c=100-h into the quadratic formula and solve for t.
22±(-22)2-4⋅(-16⋅(100-h))2⋅-16
Simplify.
Simplify the numerator.
Raise -22 to the power of 2.
t=22±484-4⋅(-16⋅(100-h))2⋅-16
Apply the distributive property.
t=22±484-4⋅(-16⋅100-16(-h))2⋅-16
Multiply -16 by 100.
t=22±484-4⋅(-1600-16(-h))2⋅-16
Multiply -1 by -16.
t=22±484-4⋅(-1600+16h)2⋅-16
Apply the distributive property.
t=22±484-4⋅-1600-4(16h)2⋅-16
Multiply -4 by -1600.
t=22±484+6400-4(16h)2⋅-16
Multiply 16 by -4.
t=22±484+6400-64h2⋅-16
t=22±6884-64h2⋅-16
Factor 4 out of 6884-64h.
Factor 4 out of 6884.
t=22±4(1721)-64h2⋅-16
Factor 4 out of -64h.
t=22±4(1721)+4(-16h)2⋅-16
Factor 4 out of 4(1721)+4(-16h).
t=22±4(1721-16h)2⋅-16
t=22±4(1721-16h)2⋅-16
Rewrite 4 as 22.
t=22±22(1721-16h)2⋅-16
Pull terms out from under the radical.
t=22±21721-16h2⋅-16
t=22±21721-16h2⋅-16
Multiply 2 by -16.
t=22±21721-16h-32
Simplify 22±21721-16h-32.
t=11±1721-16h-16
Move the negative in front of the fraction.
t=-11±1721-16h16
t=-11±1721-16h16
The final answer is the combination of both solutions.
t=-11+1721-16h16
t=-11-1721-16h16
Solve for t -16t^2-22t+100=h

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