Question

1. $|x^{2}+5x + 5|=-1$

your turn: by using two separate equations, solve each of these absolute - value equations. be sure to check and to reject extraneous solutions. the first one is done for you again. you can thank me later.

Explanation:

Step1: Recall absolute - value property

The absolute value of any real - number \(y\), denoted as \(|y|\), is defined as \(|y|=

$$\begin{cases}y, & y\geq0\\ -y, & y < 0\end{cases}$$

\), and \(|y|\geq0\) for all real numbers \(y\). In the given equation \(|x^{2}+5x + 5|=-1\).
Since the absolute value of a real - number is always non - negative, i.e., \(|x^{2}+5x + 5|\geq0\) for all real values of \(x\), and the right - hand side of the equation is \(-1<0\).

Step2: Determine the solution set

There are no real values of \(x\) that can satisfy the equation \(|x^{2}+5x + 5|=-1\).

Answer:

The solution set is \(\varnothing\) (the empty set).