+23254 x² + y² - 6x + 4y + 18
Rearrange:
x² - 6x + y² + 4y + 18
Complete the squares:
(x² - 6x ) + (y² + 4y ) + 18
(x² - 6x + 9) + (y² + 4y + 4) + 18 - 9 - 4
(x - 3)² + (y + 2)² + 5
Since (x - 3)² can never be less than 0, and neither can (y + 2)², the complete expression must always be at least 5, but can be larger than 5.
+23254 x² + y² - 6x + 4y + 18
Rearrange:
x² - 6x + y² + 4y + 18
Complete the squares:
(x² - 6x ) + (y² + 4y ) + 18
(x² - 6x + 9) + (y² + 4y + 4) + 18 - 9 - 4
(x - 3)² + (y + 2)² + 5
Since (x - 3)² can never be less than 0, and neither can (y + 2)², the complete expression must always be at least 5, but can be larger than 5.
