How do you solve $(x+8)^2(x+5)(x+7)^2>=0$ ?

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Answer 1 · 2016-07-02T20:23:57

$x in { -8, -7 } uu [-5, oo)$

Both $(x+8)^2$ and $(x+7)^2$ are squares, so always non-negative for Real values of $x$ .

As a result, the left hand side is negative when $x+5 < 0$ unless $x+7 = 0$ or $x+8=0$ , when it is zero.

Hence the inequality is satisfied when: $x in { -8, -7 } uu [-5, oo)$

graph{(x+8)^2(x+5)(x+7)^2 [-13.96, 6.04, -7.68, 2.32]}

How do you solve (x+8)^2(x+5)(x+7)^2>=0(x+8)^2(x+5)(x+7)^2>=0?