All the equations we've looked at so far began with x2. But what if there were equations that began with 2x2, 3x2, or even 900x2? That's what we're looking at today.
Solve 8x2 + 6x - 9 = 0.
Ok, so first we factorise this:
(4x - 3)(2x + 3) = 0
Remember, the numbers don't actually have to add up to 6. This is because +3 is multiplied by 4x, instead of just x, and -3 is multiplied by 2x, not just 2. However, they do still have to multiply to 9, because this is done without 'interference', as I think of it, from the numbers in front of the x.
Now we take our two possible equations, and solve them:
4x - 3 = 0
4x = 3
What we have to remember is that this isn't our final answer. We still need to divide by 4, because 3 is 4x, not x.
3/4 = 0.75
x = 0.75
Now for our second option:
2x + 3 = 0
2x = -3
x = -1.5
So x is EITHER 0.75 or -1.5 - only we don't know which. We'll look at using the quadratic formula next time. Take our quick quiz on this here:
Коментари