Question

In order to solve by completing the square, what value needs to be added to

both sides of the equation: x2 + 8x = 17? (A.8A, RC 4, RS)
A 64
B 32
C 17
D 16

can someone please explain?
​

Answer 1

16

Explanation:

To find the term needed, use the binomial formula.

`(a+b)^2 = a^2 + 2ab + b^2`

Let 8x = 2ab, a is by default x, which leaves us with:

8x = 2xb

8 = 2b

b = 4

And by the binomial formula add
`b^2` to both sides, namely 16.

`x^2 + 8x + 16 = 17 + 16\\(x+4)^2 = 33`