# How do you solve x^2-3x>=10 using a sign chart?

Dec 11, 2016

The answer is x in ] -oo,-2 ] uu [5, +oo[

#### Explanation:

Let's rewrite the equation

${x}^{2} - 3 x - 10 \ge 0$

Let $f \left(x\right) = {x}^{2} - 3 x - 10 = \left(x + 2\right) \left(x - 5\right)$

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

Let's do the 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}$$- 2$$\textcolor{w h i t e}{a a a a}$$5$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x - 2$$\textcolor{w h i t e}{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}$$x - 5$$\textcolor{w h i t e}{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}$$+$$\textcolor{w h i t e}{a a a a}$$-$$\textcolor{w h i t e}{a a a a}$$+$

So,

$f \left(x\right) \ge 0$ when x in ] -oo,-2 ] uu [5, +oo[