\( \leftarrow \)\begin{tabular}{l|l|}\hline Solve. & \( \begin{array}{l}x=\square \\ 4 x^{2}-20=0\end{array} \) \\ \( \begin{array}{l}\text { (Simplify your answer. Type } \\ \text { an exact answer, using } \\ \text { radicals as needed. Express } \\ \text { complex numbers in terms of } \\ i . \text { Use a comma to separate } \\ \text { answers as needed.) }\end{array} \) \\ \hline\end{tabular}

To solve the equation \(4x^2 - 20 = 0\), we first isolate the \(x^2\) term. Add 20 to both sides: \[ 4x^2 = 20 \] Next, divide both sides by 4: \[ x^2 = 5 \] Now, take the square root of both sides: \[ x = \pm \sqrt{5} \] Thus, the solutions are: \[ x = \sqrt{5}, -\sqrt{5} \]) The final answer is: \(x = \sqrt{5}, -\sqrt{5}\). Did you know that the Pythagorean theorem has its roots in ancient civilizations? The formula we used to find \(x\) mirrors the way ancient Greeks approached geometry, using the principles of squares and roots to solve their problems. It’s fascinating how math transcends time and connects cultures! If you're digging deeper into algebra, consider practicing with quadratic equations of different forms. Many students make the mistake of forgetting to account for both the positive and negative roots when taking the square root. So don’t just take half the answer—embrace both parts of your solution!