ANSWER
[tex]x\text{ = 13i or 13}\sqrt{-1}[/tex]EXPLANATION
We want to solve the equation:
[tex]x^2\text{ = -169}[/tex]To do this we will find the square root of both sides:
[tex]\sqrt{x^2}\text{ = }\sqrt{-169}[/tex]Because we can't find the square root of a negative number, we have to split the number:
[tex]\begin{gathered} x\text{ = }\sqrt{-1\cdot\text{ 169}} \\ x\text{ = }\sqrt{-1\text{ }}\cdot\text{ }\sqrt{169} \\ x\text{ = }\sqrt{-1\text{ }}\cdot\text{ 13} \\ x\text{ = 13}\sqrt{-1}\text{ or better written as 13i} \end{gathered}[/tex]Note: i is referred to as unit complex number.
