To solve the quadratic equation \( x^2 + 5x + 4 = 0 \), we can use factoring or the quadratic formula. Let's try factoring first.

We want to factor it as:

\[
(x + a)(x + b) = 0
\]

Where \( a \) and \( b \) are numbers that multiply to give \( 4 \) (the constant term) and add to give \( 5 \) (the coefficient of \( x \)).

Factors of 4: \( 1 \times 4 \)

Since \( 1 + 4 = 5 \), the factors are \( x + 1 \) and \( x + 4 \).

Thus, the equation becomes:

\[
(x + 1)(x + 4) = 0
\]

Setting each factor equal to zero:

1. \( x + 1 = 0 \Rightarrow x = -1 \)
2. \( x + 4 = 0 \Rightarrow x = -4 \)

Therefore, the solutions are:

\[
x = -1 \quad \text{and} \quad x = -4
\]

Would you like more details on this, or do you have any questions?

Here are 5 related questions:
1. How would you use the quadratic formula to solve this?
2. What is the discriminant of this quadratic equation?
3. How would the graph of \( y = x^2 + 5x + 4 \) look?
4. Can a quadratic equation have complex solutions?
5. How do you factor quadratics when the leading coefficient isn't 1?

**Tip:** Factoring works best when the equation is simple and has easy-to-find roots. If factoring seems tricky, the quadratic formula is always a reliable backup.

Learn how to solve the quadratic equation x² + 5x + 4 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factorization and the quadratic formula theorem. Suitable for students in Grades 7-9.

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