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Question
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
Solution
\[16x - \frac{10}{x} = 27\]
\[ \Rightarrow 16 x^2 - 10 = 27x\]
\[ \Rightarrow 16 x^2 - 27x - 10 = 0\]
\[ \Rightarrow 16 x^2 - 32x + 5x - 10 = 0\]
\[ \Rightarrow 16x\left( x - 2 \right) + 5\left( x - 2 \right) = 0\]
\[ \Rightarrow \left( 16x + 5 \right)\left( x - 2 \right) = 0\]
\[ \Rightarrow 16x + 5 = 0 \text { or } x - 2 = 0\]
\[ \Rightarrow x = - \frac{5}{16} \text { or } x = 2\]
Hence, the factors are 2 and \[- \frac{5}{16}\].
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