Final answer:
To solve the cubic inequality x³ +4x² ≥ -x-4, you need to move all terms to one side, simplify into a quadratic equation if possible, and then use the quadratic formula to find the roots. The roots and the intervals between them determine where the inequality is satisfied.
Step-by-step explanation:
The student's question involves solving a cubic inequality: x³ +4x² ≥ -x-4. To solve this inequality, the first step is to bring all terms to one side of the inequality sign, which gives us x³ + 4x² + x + 4 ≥ 0. The goal here is to rearrange this into a quadratic equation that equals 0, which may involve completing the square or other algebraic manipulations. Once in the standard form ax² + bx + c = 0, you can then use the quadratic formula to find the roots of the equation. In some cases, it may be possible to simplify the equation further by considering the physical or practical context of a problem where, for example, certain solutions may not make sense (such as having a negative concentration in a chemistry problem).
Specifically, if we were handling a quadratic with the form ax² + bx + c = 0, and after simplifying the cubic equation above, we would look to find the values of x for which the inequality holds true. The provided SEO keywords do not directly apply to solving cubic inequalities but generally apply to solving quadratic equations. To solve the inequality given in this question, one must look for the critical points where the expression equals zero and then test intervals to determine where the inequality is satisfied.