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What numbers must be added to complete the perfect square?​

What numbers must be added to complete the perfect square?​-example-1
User Celina
by
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1 Answer

4 votes

Answer:

256

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

User Drux
by
5.6k points