Signment \begin{tabular}{l} HW Score: 23.03\%, 11.29 of 49 points \\ \hline Solve the following equation. \\ \( \begin{array}{l}(x+14)^{2}=19\end{array} \) \\ \( \begin{array}{l}\text { Select the correct choice below and, if necessary, fill in the } \\ \text { answer box(es) to complete your choice. }\end{array} \) \\ \( \begin{array}{l}\text { A. The solution(s) is(are) } x= \\ \text { (Simplify your answer. Type an exact answer, using radicals } 1 \\ \text { as needed. Use a comma to separate answers as needed) }\end{array} \) \\ \hline\end{tabular}

To solve the equation \((x + 14)^2 = 19\), we first take the square root of both sides, giving us two equations: \(x + 14 = \sqrt{19}\) and \(x + 14 = -\sqrt{19}\). Next, we isolate \(x\): 1. From the first equation: \(x = \sqrt{19} - 14\) 2. From the second equation: \(x = -\sqrt{19} - 14\) Thus, the solutions are \(x = \sqrt{19} - 14, -\sqrt{19} - 14\). When explaining radical solutions, it's important to remember that we can express those values in decimal form if needed, but presenting them as exact answers maintains their precision! When solving quadratic equations, keeping track of positive and negative roots is crucial. A common mistake occurs when squaring both sides since it can introduce extraneous solutions. Always check your solutions by substituting them back into the original equation to verify they hold true. Happy solving!