![{(x + 3)}^{2} = 16](/tpl/images/0533/8505/c06a1.png)
Step-by-step explanation:
The given equation is
![{x}^{2} + 6x - 7 = 0](/tpl/images/0533/8505/84cab.png)
To find the equation that has the same solution, we complete the square.
Add the square of half the coefficient of x to both sides
![{x}^{2} + 6x + {3}^{2} = {3}^{2} + 7](/tpl/images/0533/8505/63804.png)
This becomes:
![{x}^{2} + 6x + 9 = 9 + 7](/tpl/images/0533/8505/a9aa2.png)
Factor the first three terms to get a perfect square;
![{(x + 3)}^{2} = 16](/tpl/images/0533/8505/a3f51.png)
The correct answer is C