x^2 - x - 12 = 0

(x - 4)(x + 3) = 0

Solutions:

x = -3

x = 4

The number is -3 and is also 4.

x^2 = x + 12

x^2 - x - 12 = 0

( x - 4 ) ( x + 3 ) = 0

x = 4 is a natural number

Several people have correctly said that the answer is 4, with several people showing their work.

But nobody has mentioned that the answer can also be -3

-3 squared = 9

-3 plus 12 = 9

The information in the word problem helps you build a quadratic equation which means there can be 2 answers which satisfy the equation.

So the correct answer is both 4 and -3, if this is a homework problem then your teacher will probably only award partial credit if you only give 4 as your answer.

The equation is

n^2 = n + 3

Solving that is easy:

n^2 - n - 12 = 0 = (n-4)(n+3)

So there are two numbers, n=4 or n = -3

4^2 = 16 = 4 + 12

(-3)^2 = 9 = -3 + 12

The context should clarify whether you are looking only for natural numbers, making 4 "the" number, or whether they are asking for all solutions.

Let te number be 'n'

Hence

n^2 = n + 12

n^2 - n - 12 = 0

Factor

(n - 4)(n + 3) = 0

Hence the number is '4'

Verification

4^2 = 16

16 - 4 = 12

4

x² = x + 12, so x² - x - 12 = 0, so x² - 4x + 3x - 12 = 0, so x(x-4) + 3(x-4) = 0, so (x+ 3)(x-4) = 0, x = 4. (the negative value may be omitted)

4*4=16

k^2 = 12 + k :: Note is means "=" sign, more than means "+"

Polynomial equation set equal to zero to factor:

k^2 - k - 12 = 0

Factor:

(k - 4)(k + 3) = 0

Set each quantity in parentheses equal to zero by zero product rule:

So k = -3, k = 4 are the solutions.

They say the "number" like there is only one, so take the positive one: k = 4

It's 4. The square of 4 is 16, which is 1 more than 4.

But I did that in my head. You'll have to come up with the appropriate equation. You know, "X squared =….")

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