c) \( x^{2}-32+60=0 \)

Did you know that quadratic equations, like the one you've presented, have been known and studied since ancient times in civilizations such as Babylon and Egypt? They laid the groundwork for algebra by developing methods to solve these equations, although they didn't use the same notation we do today! The geometric interpretations they explored were fundamentally about finding areas and lengths, much like solving for the roots of a quadratic. Once you rearrange the equation \(x^{2} - 32x + 60 = 0\), you can apply the quadratic formula: \(x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}\). Plugging in \(a = 1\), \(b = -32\), and \(c = 60\), you can find solutions for \(x\). A common mistake is forgetting to square the \(b\) value correctly or miscalculating the discriminant, so double-check your arithmetic for flawless results!