How do I solve x^2+6x+8=0?
Ok, so we would call this a quadratic equation because it is written in the form of ax^2+bx+c=0 (in our case, a=1, b=6, c=8).Luckily, this type of quadratic equation can be factorised, so we can solve it easily!Ok, so we're trying to factorise x2+6x+8=0 so that it is in the form of (x+p)(x+q)=0.Let's try expanding (x+p)(x+q)=0.If you multiply the brackets together, you're left with:x2+px+qx+pq=0We can tidy this up a little bit to give us:x2+(p+q)x+pq=0This looks very similar to x2+6x+8=0, doesn't it?Yes, it does! If we compare these two equations, we find out two things:p+q=6pq=8So we're looking for two numbers which when they are multiplied by each other will give 8, and when they are added together will give 6. What we're left with is that p=4 and q=2 (or the other way round, it doesn't really matter).Let's plug this back into our original equation: (x+p)(x+q)=0Of course, now we have:(x+4)(x+2)=0This is much easier to solve than what we started with!So in this case, either the first bracket is equal to 0 or the second bracket is equal to zero - this gives us two solutions for x.Either x+4=0, meaning that x=-4Or x+2=0, meaning that x=-2So now we have the answers x=-2 or x=-4Of course a quicker way to do this would be to look at x2+6x+8=0 and to find two numbers that are factors of 8 (they multiply together to make 8) and also add together to make 6.
