Let's continue with algebraic concepts. Here's an example involving solving quadratic equations:

Example: Solving a Quadratic Equation

Consider the equation: $2x^2 - 4x - 6 = 0$

Step 1: Simplify the equation

The equation is already simplified, so we can proceed with solving it.

Step 2: Use the quadratic formula

The quadratic formula is given by: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ Where:

• $a = 2$ (coefficient of $x^2$)
• $b = -4$ (coefficient of $x$)
• $c = -6$ (constant term)

Substitute these values into the quadratic formula: $x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(2)(-6)}}{2(2)}$ $x = \frac{4 \pm \sqrt{16 + 48}}{4}$ $x = \frac{4 \pm \sqrt{64}}{4}$ $x = \frac{4 \pm 8}{4}$

Step 3: Solve for $x$

Now solve for the two possible values of $x$:

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

Thus, the solutions are $x = 3$ and $x = -1$.

Would you like a detailed explanation of any of the steps or have questions about other algebraic topics?

Here are some related questions:

1. How do you factor quadratic equations?
2. Can every quadratic equation be solved using the quadratic formula?
3. What are complex roots in a quadratic equation?
4. How do you complete the square to solve a quadratic equation?
5. How does the discriminant in the quadratic formula help determine the nature of the roots?

Tip: The discriminant ($b^2 - 4ac$) in the quadratic formula tells you whether the roots are real, equal, or complex.