Question

How do you solve using the completing the square method `x^2 + 10x + 14 = -7`?

Answer 1

See below.

Explanation:

The first thing you'll want to do is take the constant terms and put them to one side of the equation. In this case, that means subtracting `14` from both sides:
`x^2+10x=-7-14`
`->x^2+10x=-21`

Now you want to take half of the `x` term, square it, and add it to both sides. That means taking half of ten, which is `5`, squaring it, which makes `25`, and adding it to both sides:
`x^2+10x+(10/2)^2=-21+(10/2)^2`
`->x^2+10x+25=-21+25`

Note that the left side of this equation is a perfect square: it factors into `(x+5)^2` (that's why they call it "completing the square"):
`(x+5)^2=-21+25`
`->(x+5)^2=4`

We can take the square root of both sides:
`x+5=+-sqrt(4)`
`->x+5=+-2`

And subtract `5` from both sides:
`x=+-2-5`
`->x=+2-5=-3` and `x=-2-5=-7`

Our solutions are therefore `x=-3` and `x=-7`.