# How do you solve x^2+21>10x using a sign chart?

##### 1 Answer
Dec 30, 2016

The answer is x in ] -oo,3 [ uu ] 7, +oo[

#### Explanation:

Let's rearrange the equation

${x}^{2} - 10 x + 21 > 0$

Let $f \left(x\right) = {x}^{2} - 10 x + 21$

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

Let's factorise

$f \left(x\right) = \left(x - 3\right) \left(x - 7\right)$

Now, we can establish 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}$$3$$\textcolor{w h i t e}{a a a a a}$$7$$\textcolor{w h i t e}{a a a a}$$+ \infty$

$\textcolor{w h i t e}{a a a a}$$x - 3$$\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}$$+$

$\textcolor{w h i t e}{a a a a}$$x - 7$$\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}$$+$

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

Therefore,

$f \left(x\right) > 0$ when  x in ] -oo,3 [ uu ] 7, +oo[