Solve the following equation for x and give your answer correct to one decimal place :

x² - 8x + 5 = 0

Comparing x² - 8x + 5 = 0 with ax² + bx + c = 0 we get,

a = 1, b = -8 and c = 5.

We know that,

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

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

$\Rightarrow x = \dfrac{-(-8) \pm \sqrt{(-8)^2 - 4.(1).(5)}}{2(1)} \\[1em] = \dfrac{8 \pm \sqrt{64 - 20}}{2} \\[1em] = \dfrac{8 \pm \sqrt{44}}{2} \\[1em] = \dfrac{8 \pm 2\sqrt{11}}{2} \\[1em] = 4 \pm \sqrt{11} \\[1em] = 4 + \sqrt{11} \text{ and } 4 - \sqrt{11} \\[1em] = 4 + 3.3 \text{ and } 4 - 3.3 \\[1em] = 7.3 \text{ and } 0.7$

Hence, x = 7.3 and 0.7