Question: Question 4 (2 points) Solve the quadratic equation by completing the square. \[ x^2 + 6x + 7 \]…

Question 4 (2 points)

Solve the quadratic equation by completing the square.

\[ x^2 + 6x + 7 \]

• \( x = 3 \)
• \( x = 1, x = 5 \)
• \( x = -3, x = -2 \)
• \( x = -1.586, x = -4.414 \)

Question 5 (1 point)

Solution

Step 1: Start with the equation \[ x^2 + 6x + 7 = 0 \] Step 2: Move the constant term to the other side \[ x^2 + 6x = -7 \] Step 3: Complete the square by adding \(\left(\frac{6}{2}\right)^2 = 9\) to both sides \[ x^2 + 6x + 9 = 2 \] Step 4: Rewrite the left side as a perfect square \[ (x + 3)^2 = 2 \] Step 5: Take the square root of both sides \[ x + 3 = \pm \sqrt{2} \] Step 6: Solve for \(x\) \[ x = -3 \pm \sqrt{2} \] Approximating \(\sqrt{2} \approx 1.414\), we get \[ x \approx -3 + 1.414 = -1.586 \] \[ x \approx -3 - 1.414 = -4.414 \] Therefore, the correct answer is option 4: \(x = -1.586\), \(x = -4.414\).