Solve the following equation for x, giving your answer correct to 3 decimal places :

2x² + 11x + 4 = 0

Comparing 2x² + 11x + 4 = 0 with ax² + bx + c = 0 we get,

a = 2, b = 11 and c = 4.

We know that,

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

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

$\Rightarrow x = \dfrac{-(11) \pm \sqrt{(11)^2 - 4.(2).(4)}}{2(2)} \\[1em] = \dfrac{-11 \pm \sqrt{121 - 32}}{4} \\[1em] = \dfrac{-11 \pm \sqrt{89}}{4} \\[1em] = \dfrac{-11 \pm 9.434}{4} \\[1em] = \dfrac{-11 + 9.434}{4} \text{ or } \dfrac{-11 - 9.434}{4} \\[1em] = \dfrac{-1.566}{4} \text{ or } \dfrac{-20.434}{4} \\[1em] = -0.392 \text{ or } -5.109$

Hence, x = -0.392 or -5.109