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

Step 1 should be

Bring the constant to the other side and divide the whole equation with 6 resulting to

x2 + 4x = -7/6

Answer 2

Step 1 should be
Bring the constant to the other side and divide the whole equation with 6 resulting to
x2 + 4x = -7/6

Step 3 should be
Complete the square by dividing the coefficient of x by 2, squaring it and adding the result to both sides of the equation.
x2 + 4x + 4 = -7/6 + 4

Step 4 should be
Factor the quadratic equation and simplify
(x+2)2 = -17/6

Step should be
Get the square root of booth sides and solve for the values of x
x+2 = +-√(102) / 6
So,
x = -2 + √(102) / 6 and x = -2 - √(102) /3