# How do solve x^2+6x>=0 and write the answer as a inequality and interval notation?

Nov 24, 2016

The solutions are $x \le - 6$ and $x \ge 0$

or x in] -oo,-6 ] uu [0, oo[

#### Explanation:

Let $f \left(x\right) = {x}^{2} + 6 x$

Let's factorise the equation

${x}^{2} + 6 x = x \left(x + 6\right)$

The values when $f \left(x\right) = 0$ are $x = 0$ and x=-6

Let's do a sign chart

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a}$$- \infty$$\textcolor{w h i t e}{a a a a}$$- 6$$\textcolor{w h i t e}{a a a a a}$$0$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x$$\textcolor{w h i t e}{a a a a a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$x + 6$$\textcolor{w h i t e}{a a a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$+$

$\textcolor{w h i t e}{a a a a}$$f \left(x\right)$$\textcolor{w h i t e}{a a a a a a a}$$+$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

Therefore $f \left(x\right) \ge 0$
when, $x \le - 6$ and $x \ge 0$

x in] -oo,-6 ] uu [0, oo[

graph{x^2+6x [-20.27, 20.27, -10.14, 10.14]}