To solve the quadratic equation \( x^2 + 7x - 30 = 0 \), we can use the quadratic formula:

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

Where the general form of a quadratic equation is \( ax^2 + bx + c = 0 \). Here:
- \( a = 1 \)
- \( b = 7 \)
- \( c = -30 \)

### Step 1: Apply the values into the quadratic formula
\[
x = \frac{-7 \pm \sqrt{7^2 - 4(1)(-30)}}{2(1)}
\]

### Step 2: Simplify under the square root
\[
x = \frac{-7 \pm \sqrt{49 + 120}}{2}
\]
\[
x = \frac{-7 \pm \sqrt{169}}{2}
\]

### Step 3: Take the square root of 169
\[
x = \frac{-7 \pm 13}{2}
\]

### Step 4: Solve for both roots
1. \( x_1 = \frac{-7 + 13}{2} = \frac{6}{2} = 3 \)
2. \( x_2 = \frac{-7 - 13}{2} = \frac{-20}{2} = -10 \)

### Solution:
The two solutions are:
\[
x = 3 \quad \text{or} \quad x = -10
\]

Would you like more details on this process or have any other questions?

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Here are 5 related questions to explore:
1. How can you verify the solutions by factoring the quadratic equation?
2. What are the characteristics of the graph of \(x^2 + 7x - 30\)?
3. How do we know if a quadratic equation has real or complex solutions?
4. Can we use completing the square method for this equation? How?
5. How do you apply the discriminant to analyze quadratic equations?

**Tip**: The discriminant (\(b^2 - 4ac\)) helps determine the nature of the solutions for any quadratic equation!

Discover how to solve the quadratic equation x^2 + 7x - 30 = 0 using the quadratic formula. This detailed step-by-step guide explains key algebraic concepts like the quadratic equation and discriminant, perfect for students in Grades 8-10.

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