Question

Solve the following quadratic equations by factorization:

\[16x - \frac{10}{x} = 27\]

Answer 1

\[16x - \frac{10}{x} = 27\]

\[ \Rightarrow 16 x^2 - 10 = 27x\]

\[ \Rightarrow 16 x^2 - 27x - 10 = 0\]

\[ \Rightarrow 16 x^2 - 32x + 5x - 10 = 0\]

\[ \Rightarrow 16x\left( x - 2 \right) + 5\left( x - 2 \right) = 0\]

\[ \Rightarrow \left( 16x + 5 \right)\left( x - 2 \right) = 0\]

\[ \Rightarrow 16x + 5 = 0 \text { or } x - 2 = 0\]

\[ \Rightarrow x = - \frac{5}{16} \text { or } x = 2\]

Hence, the factors are 2 and \[- \frac{5}{16}\].