The Square Of A Number Is Six More Than The Number. Can You Find The Number. How Do You Work This?


2 Answers

Oddman Profile
Oddman answered
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.

(-2)2 = 4  is six more than -2
(3)2 = 9  is six more than 3
Anonymous Profile
Anonymous answered
Let the number is x.
Then, x^2 = x+6
x = -2,3

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