# How do you solve the equation x^2+169=0?

Apr 16, 2017

NO REAL SOLUTIONS but rather complex solutions:

$x = - 13 i , 13 i$

#### Explanation:

Isolate the ${x}^{2}$ by subtracting 169 from both sides...

${x}^{2} + \cancel{169 - 169} = 0 - 169 \to {x}^{2} = - 169$

Now take the square root of both sides to the $x$

$\sqrt{{x}^{2}} = \sqrt{- 169} \to x = \pm \sqrt{- 169}$

Note: there are NO REAL SOLUTIONS! but rather two complex solutions denoted by the symbol $i$

So $x = - 13 i , 13 i$