I'm having trouble with this. I could swear everything is done right, but then I get to the end and substitute in the values to the original formulas and they don't come out correctly.
Please help =[
haha, what you wrote is kind of confusing.
are your two equations
$\displaystyle 5 = p(q - 1)$ ...............(1)
$\displaystyle 12.5 = p(q^2 - 1)$ ..........(2)
if so, what you did is overkill. note that $\displaystyle q^2 - 1$ is the difference of two squares. so,
$\displaystyle 12.5 = p(q - 1)(q + 1)$
wait! what's this?!
$\displaystyle 12.5 = {\color{red}p(q - 1)}(q + 1)$
now where have i seen that before?
you made a classic mistake. but of course, it drives math nuts...well, nuts.
you pulled a $\displaystyle (x + y)^2 = x^2 + y^2$ thing. that is WRONG! and yes, infuriating
$\displaystyle (x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2$
where did you do this? you wrote $\displaystyle \bigg(\frac 5p + 1 \bigg)^2 = \frac {25}{p^2} + 1$. that is wrong
$\displaystyle \bigg( \frac 5p + 1 \bigg)^2 = \frac {25}{p^2} + \frac {10}p + 1$