Find two consecutive positive integers such that the sum of their squares is 181

Find two consecutive positive integers such that the sum of their squares is 181

consecutive positive integers: x and x+1

(x) ² + (x+1) ² = 181

x² + (x² + 2x + 1) = 181 (expanded (x+1) ²)

2x²+2x+1=181 (simplified)

2x²+2x+1-181=181-181 (subtraction property)

2x²+2x-180=0

Factor to solve for x

2x²+2x-180=0

2 (x+10) (x-9) = 0

2≠0

x+10=0

x+10-10=0-10

x=-10 number must be a positive integer, cannot use - 10

x-9=0

x-9+9=0+9

x=9 we can use this one, it is positive

x=9 and x+1=9+1=10

two consecutive positive integers such that the sum of their squares is 181 are:

9 and 10

9²+10²=181

81+100=181

181=181