# How do you solve the inequality x^2+x+1>=0 and write your answer in interval notation?

Mar 23, 2017

The solution is x in ]-oo, +oo[

#### Explanation:

Let

$f \left(x\right) = {x}^{2} + x + 1$

We complete the square,

$f \left(x\right) = {x}^{2} + x + \frac{1}{4} + \frac{3}{4}$

$f \left(x\right) = {\left(x + \frac{1}{2}\right)}^{2} + \frac{3}{4}$

$\forall x \in \mathbb{R} , f \left(x\right) > 0$