Chapter 4.8, Problem

To determine

To Find: The solution of the inequality algebraically

Answer

  $-2or-5$

Explanation of Solution

Given:

  $x^2+7x\ge -10$

Formula Used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using factorization method.

Calculation:

  $\begin{array}{l}{x}^2+7x\ge -10\\ \Rightarrow x^2+7x+10\ge 0\\ \Rightarrow x^2+5x+2x+10\ge 0\\ \Rightarrow x\left(x+5\right)+2\left(x+5\right)\ge 0\\ \Rightarrow \left(x+5\right)\left(x+2\right)\ge 0\\ \text{for equal to zero}\\ x=-2or-5\end{array}$