How do you solve x^2 + 4 = 0 by completing the square?

Mar 31, 2017

$x = \pm 2 i$

Explanation:

${x}^{2} + 4 = 0 \to {x}^{2} = - 4$

Since ${x}^{2} \ge 0 \forall x \in \mathbb{R}$
$x$ in this example must be complex

$x = \pm \sqrt{- 4}$

$x = \pm 2 \cdot \sqrt{- 1}$

$x = \pm 2 i$