Question

solve x^2+2x<8

Answer 1

first, pretend as if the < sign is not there
Simplifying
x2 + 2x + -8

Reorder the terms:
-8 + 2x + x2

Factor a trinomial.
(-4 + -1x)(2 + -1x)


now put in the sign
-4<x<2 <--- final result

Answer 2

for a quadratic (degree 2) inequality, you must have zero on one side. start with
\[x^2+2x-8<0\] then factor to get
\[(x+4)(x-2)<0\]
notice that the zeros are at -4 and 2 and that
\[y=x^2+2x-8\] is a parabola that faces up, so it will be negative between the zeros and positive outside them (negative means below x - axis, positive above)

Answer 3

you want "negative" (less than zero) so answer is
\[-4<x<2\] but of course you also know where it is positive, namely
\[x<-4\] or
\[x>2\] so you have really solved more than just asked for