Answer:
256
Step-by-step explanation:
Let the number be k
Thus, the equation can be written as:
x² – 32x + k
From the above,
a = 1
b = –32
c = k
The value of k can be obtained as follow:
b² = 4ac
(–32)² = 4 × 1 × k
1024 = 4k
Divide both side by 4
k = 1024 / 4
k = 256
Thus, 256 should be added to x² – 32x to make it a perfect square i.e
x² – 32x + 256
****Check****
x² – 32x + k
k = 256
x² – 32x + 256
x² – 16x – 16x + 256
x(x – 16) – 16(x – 16)
(x – 16)(x – 16)
(x – 16)² QED
