Find the roots by using the quadratic formula x^2+4x+13=0 x=-2pm 3i x=-2pm sqrt (17) x=1 and x=-5 x=2pm 3i

## Step 1: Identifying the coefficients<br />### The quadratic equation is given as $x^2 + 4x + 13 = 0$. We can identify the coefficients as $a=1$, $b=4$, and $c=13$.<br /><br />## Step 2: Applying the quadratic formula<br />### The quadratic formula is given by $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$. Substituting the values of $a$, $b$, and $c$, we get:<br />$x = \frac{-4 \pm \sqrt{4^2 - 4(1)(13)}}{2(1)}$<br /><br />## Step 3: Simplifying the expression<br />### Simplifying the expression under the square root:<br />$x = \frac{-4 \pm \sqrt{16 - 52}}{2}$<br />$x = \frac{-4 \pm \sqrt{-36}}{2}$<br /><br />## Step 4: Evaluating the square root of a negative number<br />### Since the value under the square root is negative, we will have complex roots. $\sqrt{-36} = \sqrt{36} \cdot \sqrt{-1} = 6i$.<br />$x = \frac{-4 \pm 6i}{2}$<br /><br />## Step 5: Simplifying to obtain the roots<br />### Dividing both the real and imaginary parts by 2:<br />$x = -2 \pm 3i$