Find the possible values of x when x^2+8x+15=0

In order to find the value of x we can first factorise the equation. To factorise a quadratic we put it in the form:(x+a)(x+b)=0When multiplying out this general term we get:x^2 + bx + ax + ab = 0This can be simplified to :x^2 + (a+b)x + ab = 0 Therefore we know that we need to find two integers that add to 8 and multiply to 15 First we find the integers that can multiply to 15: 1x15=153x5=15We can see that out of these two possibilities of integer pairs to be used in the factorisation, 3 and 5 add to give 8. Therefore : a + b = 8          ab=15a=3 b=5(x+3)(x+5)=0Therefore x+3=0 or x+5=0This rearranges to give x=-3 or x=-5