Question

How do you solve by completing the square: `x^2+6x+4=0`?

Answer 1

Solving a quadratic expression by completing the square means to manipulate the expression in order to write it in the form
`(x+a)^2=b`
So, if `b\ge 0`, you can take the square root at both sides to get
`x+a=\pm\sqrt{b}`
and conclude `x=\pm\sqrt{b}-a`.

Now, we have `(x+a)^2=x^2+2ax+a^2`. Since you equation starts with `x^2+6x`, this means that `2ax=6x`, and so `a=3`.
Adding `5` at both sides, we have
`x^2+6x+9=5`
Which is the form we wanted, because now we have
`(x+3)^2=5`
Which leads us to
`x+3=\pm\sqrt{5}` and finally `x=\pm\sqrt{5}-3`