2x² + 5x = 12? Do i just move equal sign down past 12 and then make the whole equation equal zero?

Question

hartnn · Answer

yes, you can do that by subtracting 12 from both sides.

anonymous · Answer

so 2x² + 5x +12= 0

Then subtracting 12

2x^2 +5x= -12. I'm sorry I am way off

hartnn · Answer

like this :
2x² + 5x = 12
subtracting 12 from both sides
2x² + 5x-12 = 12-12
2x² + 5x -12=0
got this ?

anonymous · Answer

yes ok

hartnn · Answer

now do you know how to solve quadratic equations ?

hartnn · Answer

by factoring ?

anonymous · Answer

Can you walk me through it?

hartnn · Answer

sure, in general for $ax^2+bx+c=0$
to factor, we search 2 numbers whose product is a*c and sum is 'b'
so, for your Q, 2x² + 5x -12=0
can you think of 2 numbers with product -24 and sum = 5 ?

anonymous · Answer

8

anonymous · Answer

and um, no I cant think of the other. Im clueless

hartnn · Answer

you got one number as 8 ! thats correct, now for sum to be 5, the other number must be 5-8 =-3, right ?

hartnn · Answer

check, product = 8*(-3) =-24 = correct.

anonymous · Answer

ah damn, i was going to say that! lol

hartnn · Answer

good, so now you can split the middle term as 5x = 8x-3x
so, 2x^2+8x-3x-24=0
got this step ?

anonymous · Answer

oh wow, yes okay I am writing this all down, but yes

anonymous · Answer

This is all great thanks so much!

hartnn · Answer

welcome ^_^
but we are not done yet... :)
and sorry, it was 2x^2+8x-3x-12=0  (not -24)
next  thing is to factor out  
from 1st 2 terms : 2x^2+8x , factor out 2x, what u get ?

hartnn · Answer

you there ? 
having any trouble? or doubts?

anonymous · Answer

Sorry! My computer died on me last night and I had to fully charge it over night!

anonymous · Answer

2x(x + 4) - 3(x + 4)
= (2x - 3)(x + 4) ??

hartnn · Answer

thats correct :)

hartnn · Answer

now do you have to solve for x ? or just factorize ?