If the equation x² + ax + 16 = 0 has two equal real roots, then what is the value of a?

The given equation is: x² + ax + 16 = 0

From the given equation, a = 1,  b = a,  c = 16

It is known that if the quadratic equation ax² + bx + c = 0 has two equal real roots, then its discriminant, b² − 4ac, is equal to 0.

∴ b² − 4ac = 0

⇒ (a)² − 4 (1) (16) = 0

⇒ a² − 64 = 0

⇒ a² = 64

⇒ a = ±8

Thus, the value of a is ±8.