Let N be the number. Write an equation that says what your words say.
N2 = 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.
N2 - 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.)
N2 - N - 6 = (N+2)(N-3) = 0
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)2 = 4 is six more than -2
(3)2 = 9 is six more than 3
N2 = 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.
N2 - 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.)
N2 - N - 6 = (N+2)(N-3) = 0
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)2 = 4 is six more than -2
(3)2 = 9 is six more than 3
