SOLUTION: I want to see the steps in solving the following equation for the unknown T: (C*T)/2 = sqrt(L^2 + ((V*T)/2)^2) sqrt=square root It has been presented as a "simple" process

Algebra ->  Radicals -> SOLUTION: I want to see the steps in solving the following equation for the unknown T: (C*T)/2 = sqrt(L^2 + ((V*T)/2)^2) sqrt=square root It has been presented as a "simple" process      Log On


   

Question 845803: I want to see the steps in solving the following equation for the unknown T:
(C*T)/2 = sqrt(L^2 + ((V*T)/2)^2)
sqrt=square root
It has been presented as a "simple" process, however, it has been 50 years since I had Algebra and for the life of me I cannot see how to solve for T.
Thanks you.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%28C%2AT%29%2F2+=+sqrt%28L%5E2+%2B+%28%28V%2AT%29%2F2%29%5E2%29

Raise both members to the 2 power ( meaning square both sides).
%28CT%2F2%29%5E2=L%5E2+%2B+%28%28V%2AT%29%2F2%29%5E2

Add the additive inverse of %28%28VT%29%2F2%29%5E2 to both sides.
%28CT%2F2%29%5E2-%28%28VT%29%2F2%29%5E2=L%5E2
Steps beyond here can vary but should be mostly consistent with this:

Apply rule of exponents for the left member.
%28C%2F2%29%5E2%2AT%5E2-%28V%2F2%29%5E2%2AT%5E2=L%5E2; notice the two terms of T^2 in the left member.

Combine like-terms, or think of it as the reverse of the Distributive Property.
%28%28C%5E2%29%2F4-%28V%5E2%29%2F4%29T%5E2=L%5E2

Simplify the rational expression factor.
%28%28C%5E2-V%5E2%29%2F4%29T%5E2=L%5E2

Multiply both members by multiplicative inverse of the rational expression
(Being shown more fully):
%284%2F%28C%5E2-V%5E2%29%29%28%28C%5E2-V%5E2%29%2F4%29T%5E2=%284%2F%28C%5E2-V%5E2%29%29L%5E2
1%2AT%5E2=%284L%5E2%29%2F%28C%5E2-V%5E2%29
T%5E2=%284L%5E2%29%2F%28C%5E2-V%5E2%29

Raise both members to the 1%2F2 power.
highlight%28highlight%28highlight%28T=2L%2Fsqrt%28C%5E2-V%5E2%29%29%29%29
.
and to be strictly correct... OR highlight%28T=-2L%2Fsqrt%28C%5E2-V%5E2%29%29.
Both of them are solved for T.


A few minor steps may have been omitted, because they might seem as too obvious and unnecessary to be shown, but these as shown should be clear enough for your understanding.
-
Note also, some people may not want an irrational expression in the denominator and so would want to rationalize the denominator.