Solve the following equation for x, giving your answer correct to 3 decimal places :

x² - 16x + 6 = 0

Comparing x² - 16x + 6 = 0 with ax² + bx + c = 0 we get,

a = 1, b = -16 and c = 6.

We know that,

x = $\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

Substituting values of a, b and c in above equation we get,

$\Rightarrow x = \dfrac{-(-16) \pm \sqrt{(-16)^2 - 4.(1).(6)}}{2(1)} \\[1em] = \dfrac{16 \pm \sqrt{256 - 24}}{2} \\[1em] = \dfrac{16 \pm \sqrt{232}}{2} \\[1em] = \dfrac{16 \pm 15.232}{2} \\[1em] = \dfrac{16 + 15.232}{2} \text{ or } \dfrac{16 - 15.232}{2} \\[1em] = \dfrac{31.232}{2} \text{ or } \dfrac{0.768}{2} \\[1em] = 15.616 \text{ or } 0.384$

Hence, x = 15.616 or 0.384