(2) \( 36 x^{2}-84 x+49= \)

Let's dig into this quadratic equation! The given equation can be simplified by factoring. Notice that \(36\), \(84\), and \(49\) are perfect squares and can be rewritten as \((6x - 7)^2 = 0\). This means that the equation has a double root at \(x = \frac{7}{6}\), making it a perfect candidate for applications in parabolic motion or optimization problems! For those diving into quadratic equations, a common mistake is forgetting to set the equation to zero before attempting to factor or use the quadratic formula. Always remember to rearrange your equations; it’s the key to solving them smoothly! It’s also important to check for perfect square trinomials, as they can save you time and lead directly to solutions.