To solve the quadratic equation:

$x^2 - 3x - 4 = 0$

we can use the quadratic formula, which is given by:

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

For our equation, the coefficients are:

• $a = 1$
• $b = -3$
• $c = -4$

1. Calculate the discriminant: $b^2 - 4ac = (-3)^2 - 4 \cdot 1 \cdot (-4)$ $= 9 + 16$ $= 25$

2. Apply the quadratic formula: $x = \frac{-(-3) \pm \sqrt{25}}{2 \cdot 1}$ $= \frac{3 \pm 5}{2}$

3. Solve for both values of $x$:

   • For $x = \frac{3 + 5}{2}$: $x = \frac{8}{2} = 4$

   • For $x = \frac{3 - 5}{2}$: $x = \frac{-2}{2} = -1$

Therefore, the solutions are: $x = 4 \quad \text{and} \quad x = -1$

Would you like a more detailed explanation of the solution?

Here are five related questions to consider:

1. How would the solutions change if the constant term in the equation were different?
2. Can you factorize $x^2 - 3x - 4$ directly instead of using the quadratic formula?
3. What are the roots of the equation $x^2 - 3x + 4 = 0$?
4. How does the discriminant tell us about the nature of the roots?
5. What are the vertex and axis of symmetry of the parabola $y = x^2 - 3x - 4$?

Tip: When solving quadratics, try factoring first if the equation appears to have simple integer roots.