Solve for the variable

m^2 + 2m +3 > = 0

To solve the inequality \(m^2 + 2m + 3 \geq 0\), we need to find the values of \(m\) that satisfy the inequality.

First, let's find the roots of the quadratic equation \(m^2 + 2m + 3 = 0\). In this case, the equation does not factorize easily, so we can use the quadratic formula:

\[m = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]

Comparing the equation \(m^2 + 2m + 3 =0\) to \(am^2 + bm + c = 0\), we have \(a = 1\), \(b = 2\), and \(c = 3\).

Using the quadratic formula, we can calculate the roots of the equation:

\[m = \frac{-2 \pm \sqrt{(2^2) - 4(1)(3)}}{2(1)}\]
\[m = \frac{-2 \pm \sqrt{4 - 12}}{2}\]
\[m = \frac{-2 \pm \sqrt{-8}}{2}\]
\[m = \frac{-2 \pm 2\sqrt{2i}}{2}\]

Since we obtained a complex root with the imaginary unit \(i\), it means that the quadratic equation \(m^2 + 2m + 3 = 0\) has no real solutions. Therefore, there are no values of \(m\) that satisfy the equation \(m^2 + 2m + 3 > = 0\).