Let N be the number. Write an equation that says what your words say.

N

Now, you can put the equation in a form that lets you solve it a couple of different ways.

N

Looking at the factors of 6 (the constant term), you can find a couple that differ by 1 (the coefficient of N). To make the difference negative, the one with the larger magnitude must be negative. (2, 3 are such factors. We use -3, +2 in our factorization.)

N

The solutions will be values of N that make the factors equal to 0.

N = -2, N = +3

The number could be -2 or +3.

Check

(-2)

(3)

N

^{2}= 6 + N (the square of the number is 6 more than the number)Now, you can put the equation in a form that lets you solve it a couple of different ways.

N

^{2}- N - 6 = 0 (subtract N+6 from both sides. This is a standard quadratic form.)Looking at the factors of 6 (the constant term), you can find a couple that differ by 1 (the coefficient of N). To make the difference negative, the one with the larger magnitude must be negative. (2, 3 are such factors. We use -3, +2 in our factorization.)

N

^{2}- N - 6 = (N+2)(N-3) = 0The solutions will be values of N that make the factors equal to 0.

N = -2, N = +3

The number could be -2 or +3.

Check

(-2)

^{2}= 4 is six more than -2(3)

^{2}= 9 is six more than 3