Chapter 12.3, Problem 20E

To determine

To Solve: Theequation $x^2+63=0$ .

Answer to Problem 20E

The required answer is: $x=3i\sqrt{7}$ .

Explanation of Solution

Given information:

The given equation $x^2+63=0$

Calculation:

  $\begin{array}{l}{x}^2+63=0\\ x^2=-63\end{array}$

(Subtract 63 from both sides)

  $x=\sqrt{-63}$

(Perform square root on each side)

  $x=\sqrt{-1\cdot 3^2\cdot 7}$

(Product property of square roots)

  $x=3i\sqrt{7}$

(Simplify)

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