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

x^2 + 2x + 2 = 0

Thanks, Kim

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- May 29th 2008, 07:45 AMKim NuBasic 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 - May 29th 2008, 09:17 AMTheEmptySet

Since there are not factors of $\displaystyle 2=2\cdot 1$ 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

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

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

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

$

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

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

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

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 $\displaystyle \sqrt{-1}=i$ with that said....

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

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

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

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

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

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. - Jun 2nd 2008, 03:43 PMAlgebraAnswersDoesn't factor
That equation does not factor. You will need to use the quadratic formula to solve for 0.

Go to here for more info:

Quadratic equation - Wikipedia, the free encyclopedia

Hope that helps.

Now if you typed the question wrong and it's supposed to be x^2+3x+2 then it can factor to (x+2)(x+1), but the one you've typed cannot be factored. - Jun 2nd 2008, 06:26 PMTheEmptySet