<s>[INST] Is it possible to isolate p in $"a = 2bpq + 2apq + a(p^2) + 2aqq + bqq"?$ Is it possible to simplify this equation so that $p$ is isolated on one side instead of $a$? I tried factoring out $p$ on the right side, but I get stuck with the $ap^2$.
$$a = 2bpq + 2apq + ap^2 + 2aq^2 + bq^2$$
 [/INST] By solving p in this equation you get:
$p = \frac{\sqrt{a^2(-q)^2+a^2+abq^2+b^2q^2} -aq - bq}{a}$
or
$p = \frac{-\sqrt{a^2(-q)^2+a^2+abq^2+b^2q^2} -aq - bq}{a}$
EDIT:
Steps as requested:
$ap^2+2apq+2bpq+2aq^2+bq^2=a$
$p^2 + \frac{p(2aq+2bq)}{a }+ \frac{2aq^2+bq^2}{a} = 1$
$p^2 + \frac{p(2aq+2bq)}{a} = 1 - \frac{2aq^2+bq^2}{a}$
$p^2 + \frac{p(2aq+2bq)}{a} + \frac{(2aq+2bq)^2}{4a^2} = 1 + \frac{(2aq+2bq)^2}{4a^2} - \frac{2aq^2+bq^2}{a}$
$(p + \frac{(2aq+2bq)}{2a})^2 = 1 + \frac{(2aq+2bq)^2}{4a^2} - \frac{2aq^2+bq^2}{a}$
Can you take it from here?
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