Solve for x the quadratic equation x² - 4x - 8 = 0. Give your answer correct to three significant figures.

Given,

⇒ x² - 4x - 8 = 0

Comparing equation x² - 4x - 8 = 0 with ax² + bx + c = 0, we get :

a = 1, b = -4 and c = -8.

By formula,

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

Substituting values we get :

$\Rightarrow x = \dfrac{-(-4) \pm \sqrt{(-4)^2 - 4 \times (1) \times (-8)}}{2 \times (1)} \\[1em] = \dfrac{4 \pm \sqrt{16 + 32}}{2} \\[1em] = \dfrac{4 \pm \sqrt{48}}{2} \\[1em] = \dfrac{4 + \sqrt{48}}{2} \text{ or } \dfrac{4 - \sqrt{48}}{2} \\[1em] = \dfrac{4 + 6.928}{2} \text{ or } \dfrac{4 - 6.928}{2} \\[1em] = \dfrac{10.928}{2} \text{ or } \dfrac{-2.928}{2} \\[1em] = 5.464 \text{ or } -1.464$

Correcting the value of x to three significant figures.

Hence, x = {5.46, -1.46}.