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To solve the equation \(x^2 - 3x = 28\), we first move all terms to one side to set the equation to zero:

\[ x^2 - 3x - 28 = 0 \]

Next, we solve this quadratic equation by factoring. We look for two numbers that multiply to \(-28\) and add to \(-3\). These numbers are \(-7\) and \(4\):

\[ x^2 - 3x - 28 = (x - 7)(x + 4) = 0 \]

Setting each factor equal to zero gives the solutions:

\[ x - 7 = 0 \quad \Rightarrow \quad x = 7 \]
\[ x + 4 = 0 \quad \Rightarrow \quad x = -4 \]

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 ask next:
1. Can you explain the factoring method in more detail?
2. How do you solve quadratic equations using the quadratic formula?
3. Can you solve a system of linear equations?
4. What are the steps to complete the square for solving quadratic equations?
5. How do you graph a quadratic equation?

**Tip:** When solving quadratic equations, always check if factoring is possible before using the quadratic formula or completing the square, as it can save time and simplify the process.

Learn how to solve the quadratic equation x^2 - 3x = 28 step-by-step with detailed explanations and examples of factoring method. This problem involves key algebraic concepts such as quadratic equations and factoring. Suitable for high school students.

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