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

2x² - 10x + 5 = 0

Comparing 2x² - 10x + 5 = 0 with ax² + bx + c = 0 we get,

a = 2, b = -10 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,

$\Rightarrow x = \dfrac{-(-10) \pm \sqrt{(-10)^2 - 4.(2).(5)}}{2(2)} \\[1em] = \dfrac{10 \pm \sqrt{100 - 40}}{4} \\[1em] = \dfrac{10 \pm \sqrt{60}}{4} \\[1em] = \dfrac{10 \pm 2\sqrt{15}}{4} \\[1em] = \dfrac{10 \pm 7.74}{4} \\[1em] = \dfrac{10 + 7.74}{4} \text{ and } \dfrac{10 - 7.74}{4} \\[1em] = \dfrac{17.74}{4} \text{ and } \dfrac{2.26}{4} \\[1em] = 4.44 \text{ and } 0.56$

Hence, x = 4.44 and 0.56