x^2 +3n -18=0
solving for x
2006-12-19 14:37:44 · 5 answers · asked by Beverly Q 1 in Science & Mathematics ➔ Mathematics
x^2 + 3n -18 = 0
x^2 = 18 - 3n
x = sqrt(18-3n)
x is a real number when for n equal to and less than 6 since 18 - 3n is positive.
x is complex when n > 6, since 18 - 3n is negative... which is imaginary
2006-12-19 14:42:58 · answer #1 · answered by Dave C 7 · 1⤊ 0⤋
Since you have a minus sign in the 3rd term (-18) you will have one positive and one negative factor.
Since your x^2 term has a coefficient of one, the factorization of the equation will look like
(x- )(x+ ) = 0
To get the factors, what are the factors of 18 and what is a pair of them that have a difference of 3?
The factors are 1, 2, 3, 6, 9, 18.
3 and 6 have a difference of 3 and 3 x 6 is 18.
You know 1 is positive and 1 is negative, so since the coefficient of the x-term in your equation is positive 3 your factors will be
(x-3)(x+6) = 0
and solving for x gives you
x = 3 or -6
2006-12-19 22:45:56 · answer #2 · answered by standard_guy 1 · 0⤊ 0⤋
subtract 3n and add 18 to both sides, therefore
x^2 = -3n+18
then take the sqrt of both sides
x = sqrt(-3n+18)
that's pretty much all you can do.
2006-12-19 22:40:56 · answer #3 · answered by dali_lama_2k 3 · 0⤊ 0⤋
x= square root of (18-3n)
2006-12-19 22:41:48 · answer #4 · answered by ray 3 · 0⤊ 0⤋
i think there is a typo
(x+6)(x-3) if the variableis x
(n+6)(n-3) if the variable is n
2006-12-19 22:45:00 · answer #5 · answered by raj 7 · 0⤊ 0⤋