The sum of the square of a positive number and the square of 2 more than the number is 10. what is the number?

Let's say x is the number.

x = the number
(x+2)² + x² = 10
x² + 4x + 4 +x² = 10
2x² + 4x +4 = 10
-10                -10
2x² + 4x - 6 = 0
(2x+6)(x-1) = 0 Factor

Either 2x+6 = 0 or x-1 =0

2x + 6 = 0
2x = -6
x = -3

x-1 = 0
x =1

The number is either 1 or -3. Hope this helps!

X^2 - 4x +(4/2^2) + y^2 + 8y + (8/2^2) = -4 + (4/2^2) + (8/2^2)(x + 2)^2 + (y + 4)^2 = -4 + 4 + 16your center is (-2, -4) and the radius is the sqrt of -4 + 4 + 16 which is 4