21:20

In which step did Yvonne first make an error?

Yvonne is solving the quadratic equation 6x2 + 24x + 7 = 0

by completing the square. Her first four steps are shown in

the table.

Yvonne's Work

Step 1

Step 2

Step 3

Step 4

Step 1

Step 2

6x² + 24x+7-0

6x² + 24x - 7

6 (x²+4x) - 7

6 (x²+4x+4) - 3+24

6 (x+2) ²-27

Step 3

Step 4

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Step 2

Step-by-step explanation:

Given the quadratic equation 6x² + 24x + 7 = 0, the following steps must be followed when finding the roots using the completing the square method.

Step 1: Subtract 7 from both sides

6x² + 24x + 7 - 7 = 0 - 7

6x² + 24x = - 7

Step 2: divide through by the coefficient of x²

6x²/6 + 24x/6 = - 7/6

x² + 4x = - 7/6

Step 3: Add half of the coefficient of x (i. e 4/2 = 2) to both sides of the equation to complete the square of the equation x² + 4x.

x² + 4x + 2 = - 7/6 + 2

(x+2) ² = - 7/6 + 2

(x+2) ² = 5/6

Step 4: taking the square root of both sides

√ (x+2) ² = √5/6

x+2 = ±√5/6

x = - 2±√5/6

x = - 2+√5/6 and - 2-√5/6

Based on the conclusion above, it can be seen that Yvonne made the first error in step 2. Yvonne suppose to divide through by the coefficient of x² (i. e 6)