# How do you solve and write the following in interval notation: x^2 + 15x > -50?

Dec 26, 2017

$x < - 10 \mathmr{and} x > - 5$

#### Explanation:

${x}^{2} + 15 x > - 50 \iff {x}^{2} + 15 x + 50 > 0$

Let $f \left(x\right) = {x}^{2} + 15 x + 50 = \left(x + 5\right) \left(x + 10\right)$

We can easily see that if $f \left(x\right) = 0 \implies x = - 5 \mathmr{and} x = - 10$
We can also see that 'a' is positive (the form of $y = a {x}^{2} + b x + c$)

This is the x axis:

---------------------0------------------>x

We put the (-5,0) and (-10,0):

---------(-10)---------(-5)-----------0-------->x

'a' is positive, ($\textcolor{red}{+} {x}^{2} + 15 x + 50$), so it is a "smiling parabola":

$\textcolor{b l u e}{- - -} \left(- 10\right) - - - \left(- 5\right) \textcolor{b l u e}{- - - 0 - - \to}$x

So the answer is $x < - 10 \mathmr{and} x > - 5$