If a number is added to its square, the result is 72. Find the number.

Question

Its an algebra problem. Solving for the missing variable.

Answer 1

Let x = the number

 

x² + x = 72  ; when the number is added to its square the result is 72

 

Solve quadratic equation by factoring (suggested):

 

x² + x - 72 = 0

 

(x + 9)(x - 8) = 0

 

So, x = -9 OR x = 8.

 

Check: (-9)² + (-9) = 72

 

           (8)² + 8 = 72

Answer 2

Explore the squares of some numbers:

 

6 squares is 36 + 6 is not 72

 

7 squares is 49 + 7 is not 72

 

8 squared is 64 + 8 = 72