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.

Discover how to solve the quadratic equation x² - 3x = 4 using factoring. This step-by-step guide explains key algebraic concepts, such as factoring and the zero product property, making it suitable for students in Grades 8-10.

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