Chapter 4.8, Problem 38PPS

To determine

To Find: The solution of the inequality algebraically

Answer to Problem 38PPS

  $-2+i\sqrt{2}or-2-i\sqrt{2}$

Explanation of Solution

Given:

  $-6>x^2+4x$

Formula Used:

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Using factorization method.

Calculation:

  $\begin{array}{l}-6>x^2+4x\\ \Rightarrow 0>x^2+4x+6\\ a=1;\\ b=4;\\ c=6\\ x=\frac{-4\pm \sqrt{{\left(4\right)}^2-4\left(1\right)\left(6\right)}}{2\left(1\right)}\\ \Rightarrow x=\frac{-4\pm \sqrt{16-24}}{2}\\ \Rightarrow x=\frac{-4\pm \sqrt{-8}}{2}\\ \Rightarrow x=\frac{-4\pm 2i\sqrt{2}}{2}\\ \Rightarrow x=-2+i\sqrt{2}or-2-i\sqrt{2}\end{array}$