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.

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

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

Solution

To solve the quadratic equation by completing the square: Move the constant term to the other side of the equation. \[ x^2 + 6x = -7 \] Take half of the coefficient of \( x \), square it, and add to both sides. \[ x^2 + 6x + 9 = -7 + 9 \] Simplify the equation. \[ (x + 3)^2 = 2 \] Take the square root of both sides. \[ x + 3 = \pm\sqrt{2} \] Solve for \( x \). \[ x = -3 \pm \sqrt{2} \] Approximate the solutions. \[ x \approx -1.586, \quad x \approx -4.414 \] The correct solution is: 4. \( x = -1.586, x = -4.414 \)