Question

Solve the following equation for x and give, in the following case, your answer correct to 2 decimal places:

${\displaystyle 4x+\frac{6}{x}+13=0}$

Answer 1

${\displaystyle 4x+\frac{6}{x}+13=0}$

${\displaystyle \Rightarrow 4x^2+6+13x=0}$

${\displaystyle \Rightarrow 4x^2+13x+6=0}$

Here a = 4, b = 13 and c =  6

∴ ${\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}}$

= ${\displaystyle \frac{-\left(13\right)\pm \sqrt{{\left(13\right)}^2-4\left(4\right)\left(6\right)}}{2\left(4\right)}}$

= ${\displaystyle \frac{-13\pm \sqrt{73}}{8}}$

= ${\displaystyle \frac{-13\pm 8.54}{8}}$

= ${\displaystyle \frac{-13+8.54}{8}\text{and}\frac{-13-8.54}{8}}$

= – 0.56 and – 2.69