gcse further maths quadratics

From where you left off.

Our goal with quadratics is to:
(i) put everything to LHS; then
(ii) try to factorize LHS; then
(iii) the solution is "every bracket"=0, connected by "or".

You haven't done (ii) completely (Hint: Don't expand the brackets!)

I'll stop here for now, and see if you can finish it.

P.S. This is not the most efficient way, but "the efficient way" requires great care. Let's finish your solution before sharing mine.

hi
thank you so much for your reply, i really appreciate your help!

so if youre saying i need to factorise further then i have to remove 2x-9 right?
so... 2x-9[(x+5)-(2x-9)] = 0

and then one of them must = 0 as the two expressions multiply to 0, but 2x-9 can't be 0 as this would give a side length of 0.
so (x+5)-(2x-9)=0
-x +14 = 0
-x = -14
x = 14

so then side length (2x-9) would be 19?

i dont know if any of that makes sense or if its just pointless rambling but either way thats the best i can do lol
you mentioned an "efficient way"? would you mind sharing that at all?
thank you so much for your help, youre amazing

Yeah, that's correct.

Now the "efficient but dangerous way" is as you note that (2x-9) can't be zero.
So we can safely cancel (2x-9) on both sides (as we are guaranteed not dividing by zero) without going through the whole "bringing everything to LHS and factorize" ordeal.

Though on reflection, this only saves like five second, and it builds bad math habits, so uh... read with caution.