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ok so you have x2 - 3x = 4
the first thing you want to do is equal this to zero, we can do that by subtracting 4
x^2-3x-4=0
Now, like what that person said, what can you multiply to get -4, and add to get -3?
now let's guess and check. 1 * 4 = 4, but 1 + 4 = 5, ew that won't work
hmm. 1 * -4 = -4, and 1 - 4 = -3
that works!
now we use these two numbers, 1 and -4 and plug it back into the original equation (take the -3x away)
x^2+1x-4x-4
basically what we did is split the -3 apart, because you see, 1x-4x equals -3x so it's basically the same thing, but the point of doing this is that you can factor by grouping.
so lets group the first two terms, x^2 and 1x, what two numbers, or variables, go into both of these? well, x does.
x
Now what's x divided by x^2? that's just x
x ( x
now what's x divided by 1x? 1.
x ( x +1 )
you know this is correct when you use the distributive propetry and get what you use to have|dw:1323571839146:dw|
now, let's factor the other two terms, -4x and -4
these look like they both go into -4
-4
now, -4x divided by 4? just x.
-4 ( x
-4 divided by -4? 1.
-4 (x+1)
Now, lets bring it all together. the numbers in the parentheses should be the same (you got x+1 in both, so it's right.
(x+1) now let's bring over the numbers that aren't in parentheses x and -4 just put those in parentheses like (x-4)
the factored version is
(x+1)(x-4)
now, we have to equal both of these to zero and solve like a regular algebra problem to get your two solutions
x+1=0
subtract 1 from both sides
x=-1
do the same thing to the other one
x-4=0
add 4 to both sides
x=4
those are your two solutions x=-1 and x=4