Answer:
k = - 8
Step-by-step explanation:
Since the equation has equal roots then the discriminant Δ = 0 , that is
b² - 4ac = 0
Given
x² + 8x - k(x + 8) = 0 ← distribute parenthesis and simplify
x² + 8x - kx - 8k = 0
x² + (8 - k)x - 8k = 0 ← in standard form
with a = 1 , b = (8 - k) , c = - 8k
(8 - k)² - (4 × 1 × - 8k) = 0
64 - 16k + k² - (- 32k) = 0
64 - 16k + k² + 32k = 0
k² + 16k + 64 = 0
(k + 8)² = 0
k + 8 = 0 , then
k = - 8
