Solve the following equation for x and give your answer correct to two decimal places :

x² - 5x - 10 = 0

Comparing x² - 5x - 10 = 0 with ax² + bx + c = 0 we get,

a = 1, b = -5 and c = -10.

We know that,

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

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

$\Rightarrow x = \dfrac{-(-5) \pm \sqrt{(-5)^2 - 4.(1).(-10)}}{2(1)} \\[1em] = \dfrac{5 \pm \sqrt{25 + 40}}{2} \\[1em] = \dfrac{5 \pm \sqrt{65}}{2} \\[1em] = \dfrac{5 \pm 8.06}{2} \\[1em] = \dfrac{5 + 8.06}{2} \text{ and } \dfrac{5 - 8.06}{2} \\[1em] = \dfrac{13.06}{2} \text{ and } \dfrac{-3.06}{2} \\[1em] = 6.53 \text{ and } -1.53$

Hence, x = 6.53 and -1.53