To solve the quadratic equation $x^2 - 3x = 4$, follow these steps:

Step 1: Rearrange the equation

Move all terms to one side of the equation to set it equal to zero: $x^2 - 3x - 4 = 0$

Step 2: Factor the quadratic equation

We need to find two numbers that multiply to $-4$ (the constant term) and add to $-3$ (the coefficient of $x$). These numbers are $-4$ and $1$.

So, the equation factors as: $(x - 4)(x + 1) = 0$

Step 3: Solve for $x$

Set each factor equal to zero: $x - 4 = 0 \quad \text{or} \quad x + 1 = 0$

Solve each equation: $x = 4 \quad \text{or} \quad x = -1$

Final Answer

The solutions are $x = 4$ and $x = -1$.

Would you like more details or have any questions?

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Here are 5 related questions you could explore:

1. How would you solve the quadratic equation $2x^2 - 5x + 3 = 0$?
2. What is the quadratic formula and how is it applied?
3. How do you complete the square to solve a quadratic equation?
4. What are the implications of the discriminant in a quadratic equation?
5. Can you solve $x^2 - 3x + 4 = 0$ using the quadratic formula?

Tip: Always check your solutions by plugging them back into the original equation to ensure they satisfy the equation.