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The given equation is:

\[
x^2 + 2x - 5 = 0
\]

We can solve this quadratic equation using the quadratic formula, which is:

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

Here, \(a = 1\), \(b = 2\), and \(c = -5\). Substituting these values into the quadratic formula:

\[
x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-5)}}{2(1)}
\]
\[
x = \frac{-2 \pm \sqrt{4 + 20}}{2}
\]
\[
x = \frac{-2 \pm \sqrt{24}}{2}
\]
\[
x = \frac{-2 \pm 2\sqrt{6}}{2}
\]
\[
x = -1 \pm \sqrt{6}
\]

Thus, the two roots are \(x = -1 + \sqrt{6}\) and \(x = -1 - \sqrt{6}\).

The correct answers are:
- Option C: \(x = -1 + \sqrt{6}\)
- Option D: \(x = -1 - \sqrt{6}\)

Would you like more details, or do you have any questions? Here are some related questions to expand your understanding:

1. What is the significance of the discriminant in the quadratic formula?
2. How can you factor quadratic equations when the roots are rational numbers?
3. Can every quadratic equation be solved using the quadratic formula?
4. How do the values of \(a\), \(b\), and \(c\) affect the shape of a quadratic graph?
5. What are some real-world applications of solving quadratic equations?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) before solving a quadratic equation to understand the nature of its roots.

Select the two values of x that are roots of this equation: x^2 + 2x - 5 = 0

Learn how to solve the quadratic equation x^2 + 2x - 5 = 0 using the quadratic formula. This step-by-step guide walks through each part of the solution, explaining the algebraic concepts and how to find the roots. Suitable for students in Grades 7-9.

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