<s>[INST] completing the square to solve equation Is it possible to use the method of completing the square to solve the equation $2x^2+18x+21=0$ ?
I have problem with how to remove the negative sign on the right side.
 [/INST] First make the leading coefficient $1$:
$x^2 + 9x + \frac{21}{2} = 0$.
Then add and subtract $(\frac{9}{2})^2$:
$x^2 + 9x + \frac{21}{2} + (\frac{9}{2})^2 - (\frac{9}{2})^2 = 0$
Rearrange,
$x^2 + 9x + (\frac{9}{2})^2  = (\frac{9}{2})^2 - \frac{21}{2}$
Observe the LHS is a square:
$(x + \frac 92)^2 = \frac{81}{4} - \frac{42}{4} = \frac{39}{4}$
Take square root of both sides,
$x + \frac 92 = \pm \frac 12 \sqrt {39}$
Final solution:
$x = - \frac 92 \pm \frac 12 \sqrt {39}$
</s>