The equation given is:

\[
x^2 - 3x - 10 = 0
\]

This is a quadratic equation of the form \( ax^2 + bx + c = 0 \), where:
- \( a = 1 \),
- \( b = -3 \),
- \( c = -10 \).

We can solve this equation using the **quadratic formula**:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

### Step-by-step solution:

1. Identify the values for \( a \), \( b \), and \( c \):
   - \( a = 1 \),
   - \( b = -3 \),
   - \( c = -10 \).

2. Plug these values into the quadratic formula:

\[
x = \frac{-(-3) \pm \sqrt{(-3)^2 - 4(1)(-10)}}{2(1)}
\]

3. Simplify inside the square root:

\[
x = \frac{3 \pm \sqrt{9 + 40}}{2}
\]

\[
x = \frac{3 \pm \sqrt{49}}{2}
\]

\[
x = \frac{3 \pm 7}{2}
\]

4. Solve for the two possible values of \( x \):

- \( x_1 = \frac{3 + 7}{2} = \frac{10}{2} = 5 \),
- \( x_2 = \frac{3 - 7}{2} = \frac{-4}{2} = -2 \).

### Final answer:
\[
x = 5 \quad \text{or} \quad x = -2
\]

Do you need more details or have any questions about the steps?

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Here are 5 related questions:
1. How do you solve quadratic equations by factoring?
2. What are the steps to complete the square for a quadratic equation?
3. Can all quadratic equations be solved using the quadratic formula?
4. What is the discriminant in a quadratic equation, and what does it tell us?
5. How can we graph a quadratic equation and identify its roots visually?

**Tip:** The discriminant \( \Delta = b^2 - 4ac \) helps determine the number of real solutions of a quadratic equation:
- If \( \Delta > 0 \), there are two real solutions.
- If \( \Delta = 0 \), there is one real solution.
- If \( \Delta < 0 \), there are no real solutions, only complex ones.

Learn how to solve the quadratic equation x^2 - 3x - 10 = 0 with a step-by-step explanation using the quadratic formula. This guide covers key algebraic concepts, including identifying coefficients and using the quadratic formula. Ideal for students in Grades 8-10.

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