Question

What is 16 divided by X^2 equals 8 divided by X + 6?

Answer 1

Solve: $\frac{16}{x^{2}} = \frac{8}{x + 6}$

$\frac{16}{x^{2}} = \frac{8}{x + 6}$

$\text{Cross multiply: } 16(x + 6) = 8x^{2}$
$\text{Simplify: } 2(x + 6) = x^{2}$
$\text{Expand: } 2x + 12 = x^{2}$

$\text{Solve for x: } x^{2} - 2x - 12 = 0$

$\text{Use the quadratic equation: } x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$
$x = \frac{2 \pm \sqrt{4 + 48}}{2}$
$x = \frac{2 \pm \sqrt{52}}{2}$
$x = \frac{2 \pm \sqrt{13 \cdot 4}}{2}$

$x = \frac{2 \pm 2\sqrt{13}}{2}$
$\therefore x = 1 \pm \sqrt{13}$