Chapter 12.1, Problem 9WE

To determine

To solve: The equation $x^2+32=0$ and express irrational solution in simplest radical form.

Answer to Problem 9WE

There is no real number solution.

Explanation of Solution

Given information:

The given equation $x^2+32=0$ .

Calculation:

  $\begin{array}{l}\Rightarrow x^2+32=0\\ \Rightarrow x^2+32-32=0-32\end{array}$

(Subtract 32 from both sides)

  $\Rightarrow x^2=-32$

The square of any real number is always a nonnegative real number.

Therefore, there is no real number solution.