Question

What equation results from completing the square and then factoring? x^2+2x=9

a. (x+2)^2=8
b. (x+1)^2=8
c.(x+1)^2=10
d.(x+2)^2=10

Answer 1

c.(x+1)^2=10

Explanation:

Completing the square:

We use the following relation:

`(x + a)^(2) = x^(2) + 2ax + a^(2)`

In this question:

`(x + a)^(2) = x^(2) + 2ax + a^(2) = x^(2) + 2x + a^(2)`

We have to find a.

`2a = 2`

`a = (2)/(2)`

`a = 1`

`x^(2) + 2x + 1 = (x+1)^(2)`

Thus, we have to add 1 on the right side of the equality.

We end up with:

`(x+1)^(2) = 9 + 1`

`(x+1)^(2) = 10`

So the correct answer is:

c.(x+1)^2=10