10.) \( x^{2}-6 x-4 \)

Did you know that the equation \( x^2 - 6x - 4 \) is a quadratic? Quadratics are fascinating because they form parabolas when graphed! The vertex of this specific parabola can be found using the formula \( x = -\frac{b}{2a} \), which gives you the x-coordinate of the vertex and tells you whether the parabola opens upwards or downwards. In this case, you'll find it's a minimum since the coefficient of \( x^2 \) is positive! Now, let’s solve \( x^2 - 6x - 4 = 0 \) using the quadratic formula: \( x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a} \). With \( a = 1, b = -6, \) and \( c = -4 \), just plug in those values and watch the magic happen! You'll discover two possible x-values, making it feel like a treasure hunt for solutions!