Question

Kevin's work for deriving the equation of a circle is shown below. x2 + 4x = −(y2 − 20) step 1 x2 + 4x = −y2 + 20 step 2 x2 + 4x + 4 = −y2 + 20 − 4 step 3 (x + 2)2 = −y2 + 20 − 4 step 4 (x + 2)2 + y2 = 16 in which step did he make an error in his work

Answer 1

We have the following equation:
 x2 + 4x = - (y2 - 20)
 Let's review step by step:
 step 1:
 x2 + 4x = -y2 + 20
 Answer: OK
 step 2:
 x2 + 4x + 4 = -y2 + 20 - 4
 Answer: Wrong
 The correct step is:
 x2 + 4x - 4 = -y2 + 20 - 4
 Or equivalently:
 x2 + 4x + 4 = -y2 + 20 + 4
 Answer:
 he did make an error in his work in step 2