To solve the quadratic equation \( x^2 - 4x - 6 = 0 \), we can use the quadratic formula:

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

For the equation \( x^2 - 4x - 6 = 0 \), we have the following values:
- \( a = 1 \)
- \( b = -4 \)
- \( c = -6 \)

Now, applying these values to the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(1)(-6)}}{2(1)}
\]

Simplifying:

\[
x = \frac{4 \pm \sqrt{16 + 24}}{2}
\]
\[
x = \frac{4 \pm \sqrt{40}}{2}
\]
\[
x = \frac{4 \pm 2\sqrt{10}}{2}
\]
\[
x = 2 \pm \sqrt{10}
\]

Thus, the two solutions are:

\[
x = 2 + \sqrt{10} \quad \text{or} \quad x = 2 - \sqrt{10}
\]

These are the exact solutions. If you want approximate values:
\[
x \approx 2 + 3.16 = 5.16 \quad \text{or} \quad x \approx 2 - 3.16 = -1.16
\]

Would you like more details or further clarification?

Here are 5 related questions:
1. How can you factor quadratic equations when possible?
2. What does the discriminant \( b^2 - 4ac \) tell us about the nature of the roots?
3. How would the solution change if the equation had different coefficients?
4. What are the applications of solving quadratic equations in real life?
5. Can quadratic equations have complex roots, and how do you solve them?

**Tip:** Always check if a quadratic equation can be factored easily before using the quadratic formula—it might save time!

Learn to solve the quadratic equation x^2 - 4x - 6 = 0 using the quadratic formula. This detailed solution includes step-by-step calculations, explanations of algebraic concepts, and approximate decimal answers. Ideal for students in Grades 8-10 looking to master quadratic equations.

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