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.

Learn how to solve the quadratic equation x^2 + ax + b = 0 with a step-by-step solution using the quadratic formula. Understand the discriminant and its role in determining the nature of roots. Suitable for high school students and anyone interested in algebraic problem-solving.

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