# How do you solve and write the following in interval notation: x^2 + 6 <2x?

Jan 29, 2017

The solution $S = \left\{\emptyset\right\}$

#### Explanation:

Let's rewrite the equation

${x}^{2} - 2 x + 6 < 0$

We complete the squares

${x}^{2} - 2 x + 1 + 5 < 0$

${\left(x - 1\right)}^{2} + 5 < 0$

Let $f \left(x\right) = {\left(x - 1\right)}^{2} + 5$

So,

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

There is no solution to the inequality