Question

What value of c will complete the square in the expression below to make it a perfect

square trinomial?
x² + 8x + c

Answer 1

c = 16

Explanation:

We have (a + b)² = a² + 2ab + b²

x² + 8x + c is of the form a² + 2ab + b²

where x² = a²

8x = 2ab

and c = b²

⇒ x² + 8x + c = (x + √c)² which is a perfect square

x² = a² ⇒ x = a

8x = 2ab

⇒ 8x = 2xb

⇒ b = 8x/(2x)

⇒ b = 4

c = b²

⇒ c = 4²

⇒ c = 16

(x + √c)² = (x + √16)²

= (x + 4)²

= x² + 2(x)(4) + 4²

= x² + 8x + 16

Therefore, c = 16 makes the expression a perfect square