Question 962445: Hi, I could use some help with this literal equation.
Solve for T: n = aT^2-4T+m
Thank you
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! start with:
n = aT^2 - 4T + m
subtract m from both sides of the equation to get:
n - m = aT^2 - 4T
factor out the a on the right side of the equation to get:
n - m = a * (T^2 - 4/a * T)
in the preceding step you had to be a little creative because a * -4/a*T = -4*T
divide both sides of the equation by a to get:
(n-m)/a = T^2 - 4/a * T)
complete the squares on the right side of the equation to get:
(n-m)/a = (T-2/a)^2 - 4/a^2
add 4/a^2 to both sides of the equation to get:
(n-m)/a + 4/a^2 = (T-2/a)^2
take the square root of both sides of the equation to get:
sqrt((n-m)/a + 4/a^2) = T - 2/a
add 2/a to both sides of the equation to get:
sqrt((n-m)/a - 4/a^2) + 2/a = T
that's your solution.
T = sqrt((n-m)/a + 4/a^2) + 2/a
the way to check is to give a random value to a and T and m and solve for n in the original equation.
then use that value of n and the values of a and m previously chosen to solve for T in the final equation.
I did and the solution is confirmed as good.
I used:
a = 9
m = 5
t = 2
i solved for n using the original equation to get n = 33.
i then used:
a = 9
m = 5
n = 33
i solved for t using the final equation to get t = 2.
that confirmed the solution is good.
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