Answer:
[tex] {(x + 3)}^{2} = 16[/tex]
Step-by-step explanation:
The given equation is
[tex] {x}^{2} + 6x - 7 = 0[/tex]
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
[tex] {x}^{2} + 6x + {3}^{2} = {3}^{2} + 7 [/tex]
This becomes:
[tex] {x}^{2} + 6x + 9 = 9 + 7 [/tex]
Factor the first three terms to get a perfect square;
[tex]{(x + 3)}^{2} = 16[/tex]
The correct answer is C
