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The image shows a mathematical problem that needs to be solved. Here is the extracted problem:

\[ x^2 + x - 1 = 0 \]

To solve this quadratic equation, we can use the quadratic formula:

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

For the equation \( x^2 + x - 1 = 0 \), the coefficients are:

- \( a = 1 \)
- \( b = 1 \)
- \( c = -1 \)

Now, we can substitute these values into the quadratic formula:

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

Simplifying further:

\[
x = \frac{-1 \pm \sqrt{1 + 4}}{2}
\]
\[
x = \frac{-1 \pm \sqrt{5}}{2}
\]

So, the solutions are:

\[
x_1 = \frac{-1 + \sqrt{5}}{2}, \quad x_2 = \frac{-1 - \sqrt{5}}{2}
\]

These are the exact solutions to the quadratic equation.

Would you like more details or have any questions? Here are 5 related questions:

1. What are the properties of the discriminant in the quadratic formula?
2. How can you determine the nature of the roots based on the discriminant?
3. What is the significance of the quadratic formula in solving quadratic equations?
4. Can you express the solutions as decimal approximations?
5. How does completing the square compare with using the quadratic formula?

**Tip:** When solving quadratic equations, always check if the equation can be factored easily before using the quadratic formula—it might save you some time!

Learn how to solve the quadratic equation x^2 + x - 1 = 0 with a detailed step-by-step solution. This problem covers key algebraic concepts, including the quadratic formula and coefficients. Suitable for high school students.

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