how do you resolve this : n+(n)2=42

Question

The sum of a number and its square is 42

Answer 1

n + n^2 = 42

(i'm presuming that you want to find the possible values of n?)

So, subtract 42 from both sides of the equation:

n + n^2 - 42 = 0

So now you want to factorise this equation, this means you think of the possible numbers that you could multiply together to get 42.

There are many different options for this. You could chose: 42x1, 21x2, 14x3, 7x6.

But we need a value that is going to give us our equation and in this example only 7x6 will work (don't forget that the 42 is negative, and therefore one of the numbers that you place in the brackets has to be negative too):

So,  n + n^2 - 42 = (n + 7)(n - 6) = 0

(n+ 7)(n - 6) = 0 at two values of n, when n=-7 and when n=6.