How do you solve $x^2-6x+9>16$ using a sign chart?

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Answer 1 · 2017-03-01T20:37:22

The solution is $x in ]-oo,-1[uu]7,+oo[$

Let's rewrite the inequality and factorise

$x^2-6x+9-16>0$

$x^2-6x-7>0$

$(x-7)(x+1)>0$

Let $f(x)=(x-7)(x+1)$

We build the sign chart

$color(white)(aaaa)$ $x$ $color(white)(aaaa)$ $-oo$ $color(white)(aaaa)$ $-1$ $color(white)(aaaa)$ $7$ $color(white)(aaaa)$ $+oo$

$color(white)(aaaa)$ $x+1$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $+$ $color(white)(aaaa)$ $+$

$color(white)(aaaa)$ $x-7$ $color(white)(aaaaa)$ $-$ $color(white)(aaaa)$ $-$ $color(white)(aaaa)$ $+$

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

Therefore,

$f(x)>0$ , when $x in ]-oo,-1[uu]7,+oo[$

How do you solve x^2-6x+9>16x^2-6x+9>16 using a sign chart?