Question
Solve the following quadratic equations by factorization:
$16\text{x}-\frac{10}{\text{x}}=27$
$16\text{x}-\frac{10}{\text{x}}=27$
✓
Answer
$16\text{x}-\frac{10}{\text{x}}=27$
$16 x^2-10=27 x$
$16 x^2-27 x-10=0$
$16 x^2-32 x+5 x-10=0$
$16 x(x-2)+5(x-2)=0$
$(16 x+5)(x-2)=0$
$16 x+5=0 \text { or } x-2=0$
$\Rightarrow\text{x}=-\frac{5}{16}$ or $x = 2$
Hence, the factors are $2$ and $-\frac{5}{16}$
$16 x^2-10=27 x$
$16 x^2-27 x-10=0$
$16 x^2-32 x+5 x-10=0$
$16 x(x-2)+5(x-2)=0$
$(16 x+5)(x-2)=0$
$16 x+5=0 \text { or } x-2=0$
$\Rightarrow\text{x}=-\frac{5}{16}$ or $x = 2$
Hence, the factors are $2$ and $-\frac{5}{16}$
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