The expression you provided is a quadratic equation:

$x^2 + 4x + 10$

If you're looking to solve this quadratic equation, we can either factor it, complete the square, or use the quadratic formula. Since factoring doesn't seem feasible here, we'll use the quadratic formula.

The quadratic formula is:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

For the equation $x^2 + 4x + 10 = 0$, the coefficients are:

• $a = 1$
• $b = 4$
• $c = 10$

Now, plugging these values into the quadratic formula:

$x = \frac{-4 \pm \sqrt{4^2 - 4(1)(10)}}{2(1)}$ $x = \frac{-4 \pm \sqrt{16 - 40}}{2}$ $x = \frac{-4 \pm \sqrt{-24}}{2}$

Since the discriminant ($\sqrt{-24}$) is negative, the solutions will involve complex numbers. Simplifying further:

$x = \frac{-4 \pm 2i\sqrt{6}}{2}$

Now, divide both terms by 2:

$x = -2 \pm i\sqrt{6}$

Thus, the solutions are:

$x = -2 + i\sqrt{6} \quad \text{and} \quad x = -2 - i\sqrt{6}$

These are the complex roots of the equation $x^2 + 4x + 10 = 0$.

Would you like further details on how to solve this, or any additional explanation?

Here are 5 follow-up questions for you:

1. How do you factor quadratic equations when the discriminant is positive?
2. What is the meaning of complex roots in a quadratic equation?
3. How do you complete the square to solve quadratics?
4. What happens when the discriminant is zero in a quadratic equation?
5. Can you solve a cubic equation in a similar way to a quadratic one?

Tip: When you encounter a negative discriminant in the quadratic formula, you’ll know the roots are complex numbers.