The sum of the square of a positive number and the square of 2 more than the number is 74. What is the number?

Question

The sum of the square of a positive number and the square of 2 more than the number is 74. What is the number?

Answer 1

If your positive number is x

then 2 more than the number is x+2

 

x² + (x+2)² = 74

x² + x² + 4x + 4 = 74

2x² + 4x - 70 = 0

 

We can factor a 2 out of each term

 

2(x² + 2x - 35) = 0

x² + 2x - 35 = 0

 

Factors of -35 that add to 2 are (7)(-5) so this factors to:

(x+7)(x-5) = 0

 

x = -7 or x = 5

 

We are told x is positive so x=5,  x+2 = 7