Absolutely! I’d be happy to help you solve and explain a quadratic equation.

A quadratic equation is typically written in the form:

$ax^2 + bx + c = 0$

Where:

• $a$, $b$, and $c$ are constants,
• $x$ represents the variable we are solving for.

To solve a quadratic equation, we have several methods, including:

1. Factoring (when the equation is factorable),
2. Completing the square,
3. Quadratic Formula (most general and always works).

The quadratic formula is:

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

Example:

Let's solve an example quadratic equation:

$2x^2 - 4x - 6 = 0$

Here, $a = 2$, $b = -4$, and $c = -6$.

We can use the quadratic formula:

$x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-6)}}{2(2)}$

Now, we calculate:

$x = \frac{4 \pm \sqrt{16 + 48}}{4}$

$x = \frac{4 \pm \sqrt{64}}{4}$

$x = \frac{4 \pm 8}{4}$

So, we have two possible solutions:

1. $x = \frac{4 + 8}{4} = \frac{12}{4} = 3$
2. $x = \frac{4 - 8}{4} = \frac{-4}{4} = -1$

Final Solutions:

$x = 3 \quad \text{or} \quad x = -1$

Let me know if you need more details on this process or if you have another quadratic equation you'd like to solve!

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Here are a few follow-up questions for you:

1. Can you solve a quadratic equation by factoring? How does factoring work?
2. What is the discriminant in the quadratic formula and what does it tell you?
3. How does completing the square differ from using the quadratic formula?
4. How do you know if a quadratic equation can be factored easily?
5. How can you graph a quadratic function to find its roots?

Tip: If you ever encounter a quadratic equation where the discriminant ($b^2 - 4ac$) is negative, the equation has complex (imaginary) roots!