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

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Answer 1 · 2016-11-24T11:19:44

The solutions are $x<=-6$ and $x>=0$

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

Let $f(x)=x^2+6x$

Let's factorise the equation

$x^2+6x=x(x+6)$

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

Let's do a sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-6$ $color(white)(aaaaa)$ $0$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x$ $color(white)(aaaaaaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x+6$ $color(white)(aaaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaaaa)$ $+$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

Therefore $f(x)>=0$
when, $x<=-6$ and $x>=0$

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

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

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