1. **State the problem:** Solve the quadratic equation $x^2 + 6x - 14 = -2$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero: $$x^2 + 6x - 14 + 2 = 0$$ which simplifies to $$x^2 + 6x - 12 = 0$$ 3. **Use the quadratic formula:** For an equation $ax^2 + bx + c = 0$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=6$, and $c=-12$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 6^2 - 4 \times 1 \times (-12) = 36 + 48 = 84$$ 5. **Find the roots:** $$x = \frac{-6 \pm \sqrt{84}}{2}$$ Simplify $\sqrt{84}$: $$\sqrt{84} = \sqrt{4 \times 21} = 2\sqrt{21}$$ 6. **Substitute back:** $$x = \frac{-6 \pm 2\sqrt{21}}{2}$$ Cancel the common factor 2 in numerator and denominator: $$x = \frac{\cancel{2}(-3 \pm \sqrt{21})}{\cancel{2}} = -3 \pm \sqrt{21}$$ 7. **Final answer:** $$x = -3 + \sqrt{21} \quad \text{or} \quad x = -3 - \sqrt{21}$$