To solve the quadratic equation \( x^2 - x - 30 = 0 \) using the quadratic formula, follow these steps:

The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Here, the coefficients are:
- \( a = 1 \)
- \( b = -1 \)
- \( c = -30 \)

Substitute these values into the quadratic formula:

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

Simplify the expression:

\[
x = \frac{1 \pm \sqrt{1 + 120}}{2}
\]

\[
x = \frac{1 \pm \sqrt{121}}{2}
\]

\[
x = \frac{1 \pm 11}{2}
\]

This gives us two possible solutions for \( x \):

\[
x = \frac{1 + 11}{2} = \frac{12}{2} = 6
\]

\[
x = \frac{1 - 11}{2} = \frac{-10}{2} = -5
\]

Thus, the solutions are:
\[
x = 6 \quad \text{or} \quad x = -5
\]

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How would you solve \(x^2 - x - 30 = 0\) by factoring instead of using the quadratic formula?
2. What happens to the quadratic formula if the discriminant (\(b^2 - 4ac\)) is negative?
3. Can you apply the quadratic formula to solve \(2x^2 + 3x - 5 = 0\)?
4. How do the solutions of a quadratic equation relate to the graph of the corresponding quadratic function?
5. What are the implications of a zero discriminant in the quadratic formula?

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) before solving a quadratic equation, as it tells you the nature of the roots (real and distinct, real and equal, or complex).

Learn how to solve the quadratic equation x² - x - 30 = 0 step-by-step using the quadratic formula. This problem covers key algebraic concepts, including the quadratic formula and solving quadratic equations with real roots. Suitable for students in Grades 7-9.

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