To solve the quadratic equation \(x^2 + 2x - 12 = 0\), we can use the quadratic formula:

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

In this case, the coefficients are:
- \(a = 1\) (coefficient of \(x^2\)),
- \(b = 2\) (coefficient of \(x\)),
- \(c = -12\) (constant term).

### Step 1: Calculate the discriminant
\[
\Delta = b^2 - 4ac = 2^2 - 4(1)(-12) = 4 + 48 = 52
\]

### Step 2: Apply the quadratic formula
\[
x = \frac{-2 \pm \sqrt{52}}{2(1)} = \frac{-2 \pm \sqrt{52}}{2}
\]
Simplifying \(\sqrt{52} = 2\sqrt{13}\):
\[
x = \frac{-2 \pm 2\sqrt{13}}{2}
\]

### Step 3: Simplify the expression
\[
x = -1 \pm \sqrt{13}
\]

Thus, the solutions are:
\[
x_1 = -1 + \sqrt{13}, \quad x_2 = -1 - \sqrt{13}
\]

Would you like further details or clarification on any step?

Here are some related questions to practice:
1. Solve \(x^2 - 6x + 8 = 0\).
2. Solve \(2x^2 + 3x - 5 = 0\) using the quadratic formula.
3. Factor the quadratic equation \(x^2 - 9x + 20 = 0\).
4. Find the roots of \(x^2 - 4 = 0\).
5. Determine the discriminant for the equation \(3x^2 + 5x + 2 = 0\).

**Tip:** Always check the discriminant (\(b^2 - 4ac\)) to determine the nature of the roots (real or complex).

Learn how to solve the quadratic equation x^2 + 2x - 12 = 0 using the quadratic formula. This detailed step-by-step solution covers essential algebraic concepts, including calculating the discriminant and simplifying square roots. Ideal for students in Grades 9-10.

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