To solve the quadratic equation $x^2 + ax + b = 0$, we can use the quadratic formula:

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

Here are the steps:

1. Identify the coefficients: $a$ and $b$ from the given equation.
2. Substitute these coefficients into the quadratic formula.
3. Calculate the discriminant, $\Delta = a^2 - 4b$.
4. Determine the roots using the formula.

Let's solve this step-by-step:

1. The coefficients are $a$ and $b$.
2. The quadratic formula is $x = \frac{-a \pm \sqrt{a^2 - 4b}}{2}$.
3. Calculate the discriminant: $\Delta = a^2 - 4b$.

Case Analysis

• If $\Delta > 0$: There are two distinct real roots.
• If $\Delta = 0$: There is one real root (repeated root).
• If $\Delta < 0$: There are two complex roots.

Would you like to see the detailed steps for a specific example, or do you have any other questions?

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Here are five questions you might ask next:

1. How do I solve $x^2 + 5x + 6 = 0$?
2. What is the discriminant of the equation $x^2 - 4x + 4 = 0$?
3. Can you solve the quadratic equation $2x^2 + 3x - 2 = 0$?
4. How do I factor the quadratic equation $x^2 + 7x + 12 = 0$?
5. What are the roots of $x^2 + x + 1 = 0$?

Tip: Always check the discriminant first to determine the nature of the roots before solving the quadratic equation.