Question

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

Answer 1

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

Explanation:

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]}