Solve the quadratic equation $x^2 - 6x - 8 = 0$ and give your answer correct to three significant figures.

Given,

$x^2 - 6x - 8 = 0$

Comparing with $ax^2 + bx + c = 0$,

$a = 1, b = -6, c = -8$

By formula,

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

Substituting values we get :

$$\begin{aligned}\Rightarrow x = \frac{-(-6) \pm \sqrt{(-6)^2 - 4(1)(-8)}}{2(1)} \\[1em] \Rightarrow x = \frac{6 \pm \sqrt{36 + 32}}{2} \\[1em] \Rightarrow x = \frac{6 \pm \sqrt{68}}{2} \\[1em] \Rightarrow x = \frac{6 \pm 8.2462}{2}.\end{aligned}$$

Case 1:

$\Rightarrow x = \frac{6 + 8.2462}{2} = \frac{14.2462}{2} = 7.1231 ≈ 7.12.$

Case 2:

$\Rightarrow x = \frac{6 - 8.2462}{2} = \frac{-2.2462}{2} = -1.1231 ≈ -1.12.$

Hence, $\bm{x}$ = 7.12 or $\bm{x}$ = −1.12.