To solve the equation \( x^2 = 9x + 10 \), we'll follow these steps:

1. **Move all terms to one side of the equation** to set it equal to zero:
   \[
   x^2 - 9x - 10 = 0
   \]

2. **Factor the quadratic equation**:
   \[
   x^2 - 9x - 10 = (x - 10)(x + 1) = 0
   \]

3. **Solve for \( x \)** by setting each factor equal to zero:
   \[
   x - 10 = 0 \quad \text{or} \quad x + 1 = 0
   \]
   \[
   x = 10 \quad \text{or} \quad x = -1
   \]

The solutions are \( x = 10 \) and \( x = -1 \).

Would you like more details, or do you have any questions?

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Here are 8 related questions for further practice:

1. How do you solve \( x^2 - 5x - 14 = 0 \)?
2. What are the solutions for \( x^2 + 7x + 12 = 0 \)?
3. How do you solve the equation \( x^2 = 16x - 64 \)?
4. What happens if the quadratic equation cannot be factored easily?
5. How can you solve \( x^2 - 8x + 15 = 0 \) by completing the square?
6. What is the quadratic formula, and how is it used?
7. How do you determine the number of real solutions a quadratic equation has?
8. What are the vertex and axis of symmetry for \( x^2 - 9x - 10 = 0 \)?

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

Learn how to solve the quadratic equation x^2 = 9x + 10 step-by-step with detailed explanations. This problem involves factoring quadratic equations and applying the quadratic formula. Suitable for students in Grades 7-9.

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