Question

1/9x^2+11/3x=242

Answer 1

multiply thru by lcm 9x^2

1+ 33x = 242*9x^2
2178x^2 -33x -1 = 0
using formula;
x =[ --33 +- sqrt(33^" - 4 *2178*-1[ / 2*2178

Answer 2

hold on one sec

Answer 3

lets try this. let \[z = \frac{1}{3x}\] then you have
\[z^2+11z-242=0\]

Answer 4

k

Answer 5

\[(z-11)(z+22)=0\]
\[z=11\] or \[z=-22\]

Answer 6

now replace
\[z=\frac{1}{3x}\]
\[\frac{1}{3x}=11\]
\[x=\frac{1}{33}\]

Answer 7

or
\[\frac{1}{3x}=-22\]
\[x=-\frac{1}{66}\]

Answer 8

so two solutions are
\[\{\frac{1}{33},-\frac{1}{66}\}\]

Answer 9

good thinking!