1. ## Basic factoring question

Hi, my factoring is not too good. How do I factor this and solve for 0?:

x^2 + 2x + 2 = 0

Thanks, Kim

2. Originally Posted by Kim Nu
Hi, my factoring is not too good. How do I factor this and solve for 0?:

x^2 + 2x + 2 = 0

Thanks, Kim

Since there are not factors of $2=2\cdot 1$ that add up to two. This will not factor over the Rational Numbers. We can, however, complete the square(or use the quadratic formula ) to obtain solutions and factorizations.

First lets move the constant to the other side

$x^2+2x+2=0 \iff x^2+2x=-2$

To complete the square we take half of the b term b=2

$\frac{2}{2}=1$ and then we square it to get $1^1=1.
$

We now add this to both sides of the equation to get

$x^2+2x+1=-1$ now we can factor the left hand side to get

$(x+1)^2=-1$

Now to solve for zero we will get complex solutions because there is no Real number that when you square it you will get a negative one. To solve form here take the square root of both sides are remember that $\sqrt{-1}=i$ with that said....

Since you asked for a factorization we can add one to both sides to get

$(x+1)^2+1=0$ we can rewrite this as

$(x+1)^2-(-1)=0$ but $-1=i^2$ so we get

$(x+1)^2-i^2=0$ this is a difference of squares so we get

$[(x+1)-i][(x+1)+i]=0$

You can solve this from here using the zero factor principle.
Note you will get the same solutions as from above, or if you use the quadratic formula.

I hope this helps.

3. ## Doesn't factor

That equation does not factor. You will need to use the quadratic formula to solve for 0.