Question

Yvonne is solving the quadratic equation 6x2 + 24x + 7 = 0 by completing the square. Her first four steps are shown in the table. In which step did Yvonne first make an error?
Step 1
Step 2
Step 3
Step 4

Answer 1

we have

$6x^{2} + 24x + 7 = 0$

step $1$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$6x^{2} + 24x =-7$ -------> Yvonne first error( She added $7$ on one side and subtracted on the other)

step $2$

Factor the leading coefficient

$6(x^{2} + 4x) =-7$

step $3$

Complete the square. Remember to balance the equation by adding the same constants to each side

$6(x^{2} + 4x+4) =-7+24$

$6(x^{2} + 4x+4) =17$

step $4$

Rewrite as perfect squares

$6(x+2)^{2} =17$

therefore

the answer is

Step 1

Answer 2

The mistake was made in the first step. She added 7 on one side and subtracted on the other.
(sorry for the slow answer-speed. I just sliced open my ring finger and can't type fast for now)