(5x + 10)^2 - 23 = 0

Question

anonymous · Answer

I know I have to solve for x

anonymous · Answer

but I'm having trouble once I add 23

jackellyn · Answer

(5x+10)(5x+10)-23=0

FOIL and then find roots by either factoring or quadratic formula

anonymous · Answer

so far I have 25x + 50 + 50x + 100..is this correct so far?

anonymous · Answer

add like terms next right? so then I have 75x + 150..idk where to go from here

jackellyn · Answer

where is your x^2?

jackellyn · Answer

You should have
$$25x ^{2}+100x+77=0$$

anonymous · Answer

so do I subtract 77 first?

jackellyn · Answer

From this point, you can tell that it is prime so you have to use the quadratic formula to solve for x.

Do you know how to do that?

hero · Answer

I don't mean to interrupt, but @jackellyn, you're doing it the hard way.

jackellyn · Answer

Just doing it how I was taught @Hero but if you know a better way, go ahead

hero · Answer

$$(5x + 10)^2 - 23 = 0
\(5x + 10)^2 = 23
\5x+10 = \pm\sqrt{23}
\5x = \pm\sqrt{23} - 10
\x = \frac{\pm\sqrt{23}-10}{5}
$$

jackellyn · Answer

Did you understand what he did @mscrosscountry ?

anonymous · Answer

yes, this is how I was taught in class but I was just having trouble with what the next step would be once you square rooted. I understand now.