# How do you solve x^2-14x+49>=0?

Jan 26, 2017

The answer is $x \in \mathbb{R}$

#### Explanation:

Let's factorise the inequality

${x}^{2} - 14 x + 49 = \left(x - 7\right) \left(x - 7\right) = {\left(x - 7\right)}^{2} \ge 0$

Let $f \left(x\right) = {\left(x - 7\right)}^{2}$

The domain of $f \left(x\right)$ is ${D}_{f} \left(x\right) = \mathbb{R}$

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