Solve the equation x^2 + 10x + 24 = 0

So, we are dealing here with a quadratic equation as it is written in the form ax^2 + bx +c = 0 To tackle this we will firstly need to factorise the equation, we need to find two numbers that will multiply to get 24 (our c value) and and also add to get 10 (our b value). So lets think of what numbers can multiply to get 24 first: we have 12 and 2 and also 6 and 4. Lets check if these add up to 10, so our first pair 12 and 2 add to 14 which is not what we are looking for however 6 and 4 both add to make 10. We can then write our factorised quadratic as (x+4) (x+6) = 0 Now as we are equalling it to 0 we need to find solutions for x. Firstly, take the (x+4) and equal it to 0. So x + 4 = 0 will then give us -4Same with the (x+6) - x + 6 = 0 which gives us -6. So our solutions for x are -4 and -6