the square of a number minus the number is 552. find the number

Question

Please show the work for it too. My teacher did a bad job showing it and I need something to work off of

Answer 1

Let x be the number.  The square of a number (x²) minus the number (x²-x) is 552 (x²-x=552):

 

x² - x = 552

x² - x - 552 = 0

 

Factors to (you could also use the quadratic formula):

 

(x-24)(x+23) = 0

x = 24 and -23

 

Check:

24² - 24 = 576 - 24 = 552

(-23)² - (-23) = 529 + 23 = 552

 

Both numbers, 24 and -23, work.

Answer 2

Let's call the number we're looking for x.

 

Then the square of the number is x², and the square of the number minus the number is x² - x. We're told that equals 552. We can set up an equation:

 

x² - x = 552

 

To solve for x, let's move everything onto one side and then factor the quadratic:

 

x² - x - 552 = 0

(x - 24)(x + 23) = 0

x - 24 = 0    OR    x + 23 = 0

x = 24    OR    x = -23

 

That means there are two possibilities for your number: 24 and -23.

 

 

Check those answers:

 

The square of 24 minus 24 is 24² - 24 = 576 - 24 = 552. That one checks out.

The square of -23 minus -23 is (-23)² - (-23) = 529 + 23 = 552. That one checks out, too.