Answer:
9
Explanation:
You want the value that must be added to x² +6x = 7 to complete the square.
Perfect square trinomial
The square of a binomial looks like ...
(x +a)² = x² +2ax +a²
The constant term (a²) is the square of half the coefficient of the linear term:
((2a)/2)² = a²
Completing the square
The square is complete when the left side of the equation is a perfect square trinomial. We can get it to be that if we add (6/2)² = 9 to both sides of the equation.
x² +6x +9 = 7 +9 . . . . add 9 to complete the square
(x +3)² = 16 . . . . . . . the completed square