Chapter 12.3, Problem 22E

To determine

To Solve: Theequation $x^2+272=0$ .

Answer to Problem 22E

The required answer is: $x=4i\sqrt{17}$

Explanation of Solution

Given information:

The given equation $x^2+272=0$

Calculation:

  $\begin{array}{l}{x}^2+272=0\\ x^2=-272\end{array}$

(Subtract 272 from each side)

  $x=\sqrt{-272}$

(Perform square root on each side)

  $x=\sqrt{-1\cdot 4^2\cdot 17}$

(Product property of square roots)

  $x=4i\sqrt{17}$

(Simplify)

(The square root of -1 is an imaginary number represented by i)