How do you solve by completing the square and express the answers in simplest radical form: x^2+2x+4=0?

Apr 2, 2015

If ${x}^{2} + 2 x$ are the first 2 terms of a quadratic generated from an expression of the form ${\left(x + a\right)}^{2}$
then the the complete form of the quadratic must be
${x}^{2} + 2 x + 1$

Separate this part of the left side of the given equation and more the excess to the right side by subtracting it from both sides
${x}^{2} + 2 x + 1 = - 3$

Take the square root of both sides
$x + 1 = \pm \sqrt{3}$

Giving the results
$x = - 1 - \sqrt{3}$
and
$x = - 1 + \sqrt{3}$