Mariah converted the following equation into standard form.25x2 + 25y2 – 200x + 100y + 4 = 025x2 – 200x + 25y2 + 100y = –425(x2 – 8x) + 25(y2 + 4y) = –425(x2 – 8x + 16) + 25(y2 + 4y + 4) = –4 + 16 + 425(x – 4)2 + 25(y + 2)2 = 16

When completing the squares, Mariah added 16 inside the first parentheses and 4 inside the second. Because each group is multiplied by 25, those additions increase the left side by 25 × 16 = 400 and 25 × 4 = 100. She needed to add 400 and 100 to the right side, not just 16 and 4, so choice C is correct.

AI-written and checked against the verified answer.