How do you solve $x^{2} + 6 x + 9 \geq 0$ $x^2+6x+9>=0$ using a sign chart?

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Answer 1 · 2016-12-23T04:14:02

The answer is $x in RR$

We use

$(a+b)^2=a^2+2ab+b^2$

Factorise the expression

$x^2+6x+9=(x+3)^2$

Let $f(x)=(x+3)^2$

The domain of $f(x)$ is $D_f(x)=RR$

and

$AA x in RR$ , $f(x)>=0$

So,

$x in RR$

The sign chart is simple

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-3$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+3$ $color(white)(aaaa)$ $-$ $color(white)(aaa)$ $0$ $color(white)(aa)$ $+$

$color(white)(aaaa)$ $f(x)$ $color(white)(aaaaa)$ $+$ $color(white)(aaa)$ $0$ $color(white)(aa)$ $+$

Therefore,

$f(x)>=0$ when $x in RR$

How do you solve x^2+6x+9>=0x2+6x+9≥0x^2+6x+9>=0 using a sign chart?