\( \begin{array}{l}\text { QUESTION } \\ \text { Solve for } x\end{array} 4 x^{2}-4 x+1 \leq 0 \)

To solve the inequality \(4x^{2}-4x+1 \leq 0\), we can first factor the quadratic expression. Notice that it can be written as \((2x - 1)^2\). Since a square is always non-negative, \((2x - 1)^2 \leq 0\) only when the expression equals zero. This happens when \(2x - 1 = 0\), leading to \(x = \frac{1}{2}\). Therefore, the solution to the inequality is \(x = \frac{1}{2}\). For real-world application, this type of quadratic inequality appears in various fields, such as physics when analyzing motion under constraints. For example, if you were studying a projectile's height and wanted to find when it is at or below a certain height, understanding how to manipulate and solve quadratics is crucial for predicting outcomes based on initial conditions.