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# What value of $$k$$ makes the expression $$x^2-8x+k=0$$ a perfect square?

### Question

What value of $$k$$ makes the expression $$x^2-8x+k=0$$ a perfect square?

A) 2

B) 4

C) 8

D) 16

### Explanation:

$$b^2-4ac=0$$
$$b=4ac$$
Where $$b=-8,a=1$$ and $$c=k$$
$$-8^2=4×1×k$$
$$64=4k$$
Then, dividing both sides by 4
$$k=16$$

Explanation provided by Emmanuel Enwere

## Discussion (2)

• $$b^2-4ac=0$$
$$b=4ac$$
Where $$b=-8,a=1$$ and $$c=k$$
$$-8^2=4×1×k$$
$$64=4k$$
Then, dividing both sides by 4
$$k=16$$

$$k = \left( \cfrac{-8}{2} \right)^2 = (-4)^2 = 16$$