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.