Factoring

Sep 2009
51
0
\(\displaystyle 3x - \frac{7}{x} = 5\)

I dont like fractions.-_-"
 

Prove It

MHF Helper
Aug 2008
12,883
4,999
\(\displaystyle 3x - \frac{7}{x} = 5\)

I dont like fractions.-_-"
\(\displaystyle 3x - \frac{7}{x} = 5\)

\(\displaystyle x\left(3x - \frac{7}{x}\right) = 5x\)

\(\displaystyle 3x^2 - 7 = 5x\)

\(\displaystyle 3x^2 - 5x - 7 = 0\)

\(\displaystyle 3\left(x^2 - \frac{5}{3} - \frac{7}{3}\right) = 0\)

\(\displaystyle 3\left[x^2 - \frac{5}{3} + \left(-\frac{5}{6}\right)^2 - \left(-\frac{5}{6}\right)^2 - \frac{7}{3}\right] = 0\)

\(\displaystyle 3\left[\left(x - \frac{5}{6}\right)^2 - \frac{25}{36} - \frac{84}{36} \right] = 0\)

\(\displaystyle 3\left[\left(x - \frac{5}{6}\right)^2 - \frac{109}{36}\right] = 0\)

\(\displaystyle 3\left[\left(x - \frac{5}{6}\right)^2 - \left(\frac{\sqrt{109}}{6}\right)^2\right] = 0\)

\(\displaystyle 3\left(x - \frac{5}{6} + \frac{\sqrt{109}}{6}\right)\left(x - \frac{5}{6} - \frac{\sqrt{109}}{6}\right) = 0\)