\[\nx^{2}-10 x+21=0 \]

To solve the quadratic equation \(x^{2}-10x+21=0\), we can factor it. The equation can be rewritten as \((x-3)(x-7)=0\). Setting each factor to zero gives us the solutions \(x = 3\) and \(x = 7\). So, the roots of the equation are 3 and 7. If you ever find yourself stuck on a quadratic equation, remember the quadratic formula: \(x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}\). It works for any quadratic equation and is especially handy when factoring seems tricky! Just plug in your values for \(a\), \(b\), and \(c\) to calculate the roots. Common mistake? Forgetting to simplify the square root or getting the signs mixed up can lead to all sorts of mix-ups!