Certainly! Here’s a narrative explanation for completing the square to solve the quadratic equation **x² + 6x - 7 = 0**: --- To solve the quadratic equation **x² + 6x - 7 = 0** by completing the square, we follow a series of logical steps. First, I start by moving the constant term to the right side of the equation. That gives me: x² + 6x = 7 Next, I want to create a perfect square trinomial on the left side. To do this, I take the coefficient of x, which is 6, divide it by 2 to get 3, and then square it to get 9. I add this number to both sides of the equation to keep it balanced: x² + 6x + 9 = 7 + 9 Now the equation becomes: x² + 6x + 9 = 16 The left side is now a perfect square trinomial, which can be written as: (x + 3)² = 16 To solve for x, I take the square root of both sides: x + 3 = ±4 Finally, I subtract 3 from both sides to get the two possible solutions: x = 4 - 3 → x = 1 x = -4 - 3 → x = -7 So, the solutions to the equation x² + 6x - 7 = 0 by completing the square are **x = 1** and **x = -7**. In summary, completing the square involves rearranging the equation, creating a perfect square trinomial, and then solving for x. This method is especially useful when the quadratic does not factor easily. ---