Let's solve the quadratic equation:

\[
0 = x^2 + 4x - 20
\]

### Step 1: Identify coefficients
This quadratic equation is in the standard form \( ax^2 + bx + c = 0 \), where:
- \( a = 1 \)
- \( b = 4 \)
- \( c = -20 \)

### Step 2: Apply the quadratic formula
The quadratic formula is:

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

Substitute the values of \( a \), \( b \), and \( c \):

\[
x = \frac{-4 \pm \sqrt{4^2 - 4(1)(-20)}}{2(1)}
\]

\[
x = \frac{-4 \pm \sqrt{16 + 80}}{2}
\]

\[
x = \frac{-4 \pm \sqrt{96}}{2}
\]

### Step 3: Simplify the square root
\[
\sqrt{96} = 4\sqrt{6}
\]

Now substitute back:

\[
x = \frac{-4 \pm 4\sqrt{6}}{2}
\]

### Step 4: Simplify the expression
\[
x = -2 \pm 2\sqrt{6}
\]

Thus, the solutions are:

\[
x = -2 + 2\sqrt{6} \quad \text{or} \quad x = -2 - 2\sqrt{6}
\]

These are the exact solutions to the equation. Would you like the approximate decimal values as well?

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Here are 5 related questions:

1. How do you factor a quadratic equation like \( x^2 + 4x - 20 = 0 \)?
2. What is the discriminant, and how does it help determine the nature of the solutions?
3. Can all quadratic equations be solved using the quadratic formula?
4. How do you simplify square roots when solving quadratic equations?
5. How would the graph of \( y = x^2 + 4x - 20 \) look like?

**Tip**: Always check the discriminant (\( b^2 - 4ac \)) to predict if a quadratic equation has real, imaginary, or repeated solutions.

Learn how to solve the quadratic equation x^2 + 4x - 20 step-by-step. This solution demonstrates how to apply the quadratic formula, simplify square roots, and interpret the discriminant. Suitable for students in Grades 8-10.

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