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
$16\text{x}-\frac{10}{\text{x}}=27$
$16x^2 - 10 = 27x$
$16x^2 - 27x - 10 = 0$
$16x^2 - 32x + 5x - 10 = 0$
$16x(x - 2) + 5 (x - 2) = 0$
$(16x + 5)(x - 2) = 0$
$16x + 5 = 0 or x - 2 = 0$
$\Rightarrow\text{x}=-\frac{5}{16}$ or $x = 2$
Hence, the factors are 2 and $-\frac{5}{16}$
$16x^2 - 10 = 27x$
$16x^2 - 27x - 10 = 0$
$16x^2 - 32x + 5x - 10 = 0$
$16x(x - 2) + 5 (x - 2) = 0$
$(16x + 5)(x - 2) = 0$
$16x + 5 = 0 or x - 2 = 0$
$\Rightarrow\text{x}=-\frac{5}{16}$ or $x = 2$
Hence, the factors are 2 and $-\frac{5}{16}$
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