Answer:
D. (x +8)² = 86
Explanation:
You want the vertex form of the quadratic equation x² +16x = 22.
Complete the square
The square of a binomial is ...
(x +a)² = x² +2ax +a²
You will notice the constant in the binomial (a) is half the coefficient of the x-term (2a).
We "complete the square" by adding a² to both sides of the equation.
x² +16x = 22 . . . . . . . . given
x² +16x +(16/2)² = 22 +(16/2)² . . . . add the square of half the x-coefficient
x² +16x +64 = 22 +64
(x +8)² = 86 . . . . . . . matches choice D
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