Please answer the given problem. Highlight all the possible misconceptions that Robin and Nami might have. After that, provide the correct solution. Show your step-by-step solutions. (Please check all the mistakes they did in their solutions)

1. Robin and Nami were asked to transform the general form of the equation 2x3+2y'+12x -By -10 =0 to its standard form. Robin wrote this: Nami wrote this: 2x2 + 2yz+ 12x - By - 10 =0 2x2 + 2y2 + 12x - By - 10 = 0 (2x2 + 12x) + (2y2 - By) = -10 (2x2 + 12x) + (2y? - By) = 10 2(x2 + 6x) + 2(y? - 4y) = -10 2(x2 + 6x) + 2(y? - 4y) =10 2(x2 + 6x + 9) +2(y2 - 4y +4) = -10 +18 +8 2(x2 + 6x + 9) + 2(y? - 4y +4) =10+9+4 2(x + 3)? + 2(y-2)? = 16 2(x + 3)2 + 2(y -2)? = 23 2(x + 3)? 2(y -2)2 16 2(x + 3)2 2(y - 2)= 23 2 2 2 2 2 2 (x +3)2 + (y - 2)= =8 (x + 3)3 + (y- 2) = 7 23 Both Robin and Nami obtained the wrong solutions. i. Highlight the possible misconceptions that Robin and Nami might have. Provide the correct solution