Question

solve the equation by completing the square.
$x^2 + 2x + 3 = 0$
$x = \square$
(simplify your answer, including any radicals and $i$ as needed. u

Explanation:

Step1: Move constant to right

$x^2 + 2x = -3$

Step2: Complete the square

$x^2 + 2x + 1 = -3 + 1$
$(x + 1)^2 = -2$

Step3: Solve for x

$x + 1 = \pm\sqrt{-2} = \pm i\sqrt{2}$
$x = -1 \pm i\sqrt{2}$

Answer:

$-1 \pm i\sqrt{2}$