x²-2x-24 = 0
We must factor that. Here's how:
Think of all the ways to write 24 as the product of 2 integers
starting with 24·1:
24·1
12·2
8·3
6·4
Since the sign of 24 is -, subtract these out to the side:
24·1 24-1 = 23
12·2 12-2 = 10
8·3 8-3 = 5
6·4 6-4 = 2
Look at the given equation: x²-2x-24 = 0
The middle term's coefficient (in absolute value) is 2, and
it is listed above in the differences, with 6 and 4.
So we write:
(x 6)(x 4) = 0
and since the middle term is negative, put a - sign with
the larger, 6, and a + sign with the smaller 4
(x-6)(x+4) = 0
Now since the product of (x-6) and (x+4) equals 0, that means
that one of those equals 0. So we set each DISABLED_event_one= 0:
x-6 = 0; x+4 = 0
x = 6; x = -4
So there are two solutions, 6 and -4.
We check x = 6 by substituting (6) for x in the original
equation:
x²-2x-24 = 0
(6)²-2(6)-24 = 0
36-12-24 = 0
0 = 0
So x = 6 is a solution:
We check x = -4 by substituting (-4) for x in the original
equation:
x²-2x-24 = 0
(-4)²-2(-4)-24 = 0
16+8-24 = 0
0 = 0
So x = -4 is also a solution:
So we are now certain that x=6 and x=-4 are the solutions
to the given equation.
Edwin
