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The equation given is:

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

To find the roots of this quadratic equation, we can use the **quadratic formula**:

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

For this equation, the coefficients are:
- \(a = 1\)
- \(b = 3\)
- \(c = -3\)

Let's substitute these values into the quadratic formula and solve for \(x\).It seems like I can’t do more advanced data analysis right now. Please try again later. However, I can guide you through solving the quadratic equation manually if you'd like!

Would you like to go through the steps together, or try again another time?

Here are some related questions for further understanding:
1. What is the discriminant and how does it help determine the nature of roots?
2. How would the roots differ if the constant term in the equation were positive?
3. Can the quadratic formula always be used for any quadratic equation?
4. What are the alternative methods for solving quadratic equations?
5. How do irrational numbers appear in the solutions of quadratic equations?

**Tip:** When using the quadratic formula, always simplify the square root as much as possible to get the cleanest answer.

Select the two values of x that are roots of this equation: x^2 + 3x - 3 = 0

Learn how to solve the quadratic equation x^2 + 3x - 3 = 0 using the quadratic formula. This guide covers key algebraic concepts, including step-by-step solutions for finding the roots using the quadratic formula and analyzing the discriminant. Ideal for students in Grades 9-11.

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