Question

Solve:
$2x^2+3x+6=0$

Answer 1

$2x^2+3x+6=0$

$2(x^2+\frac{3}{2}x+3)=0$

$\Rightarrow x^2+\frac{3}{2}x+3=0$

$\Rightarrow x^2+2\times \frac{3}{4}x+{\left(\frac{3}{4}\right)}^2-{\left(\frac{3}{4}\right)}^2+3=0$

$\Rightarrow {(x+\frac{3}{4})}^2+3-\frac{9}{16}=0$

$\Rightarrow {(x+\frac{3}{4})}^2+\frac{48-3}{16}=0$

$\Rightarrow {(x+\frac{3}{4})}^2+\frac{48-3}{16}=0$

$\Rightarrow {(x+\frac{3}{4})}^2+\frac{45}{16}=0$

$\Rightarrow x+\frac{3}{4}=\sqrt{\frac{-9\times 5}{16}}$

$\Rightarrow x=\frac{-3}{4}\pm \frac{3\sqrt{-5}}{4}$

$\therefore x=\frac{-3\pm 3i\sqrt{5}}{4}$