SOLUTION: Hi, I could use some help with this literal equation. Solve for T: n = aT^2-4T+m Thank you

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.

RELATED QUESTIONS
solve {{{2t(t+2)=1}}} I could use some help with this problem please. Thank... (answered by stanbon)

Hi, I am studying for a test and could really use some help with this problem. I know... (answered by jim_thompson5910)

Dear Tutor, Could you please explain the procedure in solving this problem: Let... (answered by Fombitz)

LITERAL EQUATIONS: how would you solve m = 2/5y + n, for y? thank... (answered by josgarithmetic)

F=Gm1m2/r^2 SOLVE FOR m2 can some one explain this literal equation to me. Thank... (answered by Alan3354,Fombitz)

Hi, I am wondering if I could get some help with this question?? Solve for r r^2 +... (answered by solver91311)

Would you please solve some equations for me for a discussion questions. 1. 5 y -1... (answered by lwsshak3)

Hi all, I was hoping someone could show me how to solve the following quadratic equation: (answered by Edwin McCravy)

I could really use some help on how to solve the following equation for t: {{{... (answered by josgarithmetic)