Solve the following quadratic equation : x² + 4x - 8 = 0. Give your answer correct to one decimal place.

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 :

$\Rightarrow x = \dfrac{-(4) \pm \sqrt{(4)^2 - 4 \times (1) \times (-8)}}{2 \times (1)} \\[1em] = \dfrac{-4 \pm \sqrt{16 + 32}}{2} \\[1em] = \dfrac{-4 \pm \sqrt{48}}{2} \\[1em] = \dfrac{-4 + \sqrt{48}}{2} \text{ or } \dfrac{-4 - \sqrt{48}}{2} \\[1em] = \dfrac{-4 + 6.9}{2} \text{ or } \dfrac{-4 - 6.9}{2} \\[1em] = \dfrac{2.9}{2} \text{ or } \dfrac{-10.9}{2} \\[1em] = 1.45 \text{ or } -5.45$

Correcting the value of x to one decimal place.

Hence, x = {1.5, -5.5}.