To solve the equation x^2 + 6x = 7 by completing the square, you can follow these steps:
1. Start with the equation x^2 + 6x = 7.
2. To complete the square, you need to add and subtract (6/2)^2 = 9 to the left side of the equation to maintain equality. This step helps in creating a perfect square trinomial.
3. Add 9 to both sides of the equation:
x^2 + 6x + 9 = 7 + 9
(x + 3)^2 = 16
4. Rewrite the equation in the form of a perfect square:
(x + 3)^2 = 16
5. To solve for x, take the square root of both sides:
x + 3 = ±√16
6. Simplify the right side:
x + 3 = ±4
7. Solve for x by considering both positive and negative roots:
x = -3 + 4 or x = -3 - 4
x = 1 or x = -7
Therefore, the solution set of the equation x^2 + 6x = 7 is {1, -7}. This means that the correct option from the choices provided is O (-7, 1).
