The expression \(x^2 + 3x - 10\) is a quadratic equation. To find the solutions for \(x\), you can either factor the equation, complete the square, or use the quadratic formula.

Let's solve it using the quadratic formula:

The quadratic formula is:

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

For the equation \(x^2 + 3x - 10 = 0\), the coefficients are:
- \(a = 1\)
- \(b = 3\)
- \(c = -10\)

Substituting these into the quadratic formula:

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

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

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

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

Now, solving for the two possible values of \(x\):

1. \(x = \frac{-3 + 7}{2} = \frac{4}{2} = 2\)
2. \(x = \frac{-3 - 7}{2} = \frac{-10}{2} = -5\)

So, the solutions are \(x = 2\) and \(x = -5\).

Would you like more details on this process or have any questions?

Here are 5 related questions you might find useful:
1. How do you factor a quadratic equation like \(x^2 + 3x - 10\)?
2. What are the steps to complete the square for a quadratic equation?
3. How can you graph the quadratic function \(x^2 + 3x - 10\)?
4. What do the solutions of a quadratic equation represent on its graph?
5. How do you determine the axis of symmetry for the quadratic equation?

**Tip:** Always check your solutions by substituting them back into the original equation to ensure they satisfy it.

Learn how to solve the quadratic equation x^2 + 3x - 10 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula. Suitable for students in Grades 9-12.

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