How do you factor and solve #x^2+8x+15=0#?
Find roots that when added come to the middle term coefficient and when multiplied come to the last term and you'll find that
The key to factoring these kind of quadratic equations is to find 2 roots that when added up equal the coefficient of the middle term and when multiplied equal the last term.
If I'm having problems finding it, I often list out the factors of the last term and see what adds up to the middle term, like this:
(when things get complicated with negative signs and coefficients in front of the first term, this method can really help keep things organized).
Ok - we know the roots are 3 and 5:
The reason we set the left side equal to 0 is because it's easy to multiply by 0 in one term and get 0 as the overall answer. So what we do now is find out what it'll take to make x+3 = 0 and what it'll take x+5 = 0.
Let's do the x+3 first:
Now the x+5 term:
And those are your answers.