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The given equation is \( x^2 - 3x = 28 \).

To solve this quadratic equation, follow these steps:

1. **Rewrite the equation in standard form**: 
\[ x^2 - 3x - 28 = 0 \]

2. **Factor the quadratic equation**: 
We need to find two numbers that multiply to \(-28\) and add to \(-3\). These numbers are \(-7\) and \(4\). Thus, we can factor the quadratic as:
\[ (x - 7)(x + 4) = 0 \]

3. **Solve for \( x \)**:
Set each factor equal to zero:
\[ x - 7 = 0 \quad \text{or} \quad x + 4 = 0 \]

Therefore, the solutions are:
\[ x = 7 \quad \text{or} \quad x = -4 \]

So, the solutions to the equation \( x^2 - 3x = 28 \) are \( x = 7 \) and \( x = -4 \).

Would you like more details or have any questions? Here are 5 questions you might want to ask:

1. Can you explain how to factor quadratic equations in more detail?
2. What are the different methods to solve quadratic equations?
3. How can I verify the solutions of a quadratic equation?
4. Can you show me how to solve this equation using the quadratic formula?
5. What are the applications of quadratic equations in real life?

**Tip:** When factoring quadratic equations, always look for two numbers that multiply to the constant term and add up to the coefficient of the linear term.

Learn how to solve the quadratic equation x^2 - 3x = 28 with a detailed step-by-step solution. This problem covers key algebraic concepts, including factoring and solving quadratic equations. Suitable for students in Grades 9-12.

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