To find the roots of the quadratic equation \( x^2 + 2x - 30 = 0 \), we can use the **quadratic formula**:

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

For the equation \( x^2 + 2x - 30 = 0 \), we have:

- \( a = 1 \)
- \( b = 2 \)
- \( c = -30 \)

Now, substituting into the quadratic formula:

\[
x = \frac{-2 \pm \sqrt{2^2 - 4(1)(-30)}}{2(1)}
\]

Simplify the terms inside the square root:

\[
x = \frac{-2 \pm \sqrt{4 + 120}}{2}
\]

\[
x = \frac{-2 \pm \sqrt{124}}{2}
\]

Since \( \sqrt{124} = 2\sqrt{31} \), the equation becomes:

\[
x = \frac{-2 \pm 2\sqrt{31}}{2}
\]

Finally, simplify:

\[
x = -1 \pm \sqrt{31}
\]

Thus, the two roots are:

\[
x_1 = -1 + \sqrt{31} \quad \text{and} \quad x_2 = -1 - \sqrt{31}
\]

Would you like further details or explanations?

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Here are 5 related questions:

1. How do you solve quadratic equations using factoring?
2. What is the discriminant, and how does it determine the nature of roots?
3. How would the solution change if the quadratic equation were \( x^2 + 2x + 30 = 0 \)?
4. Can you explain how to complete the square for this equation?
5. What are real and complex roots, and how do they differ?

**Tip:** The discriminant \( b^2 - 4ac \) can quickly tell you if the roots are real or complex. If it's positive, the roots are real and distinct.

Discover how to solve the quadratic equation x^2 + 2x - 30 = 0 by applying the quadratic formula. This step-by-step solution breaks down the use of algebraic concepts, the quadratic formula, and the discriminant. Ideal for students in Grades 9-10.

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