a. \( 2 x^{2}-50=0 \)

To solve the equation \( 2x^{2} - 50 = 0 \), you first want to add 50 to both sides to get \( 2x^{2} = 50 \). Then, divide both sides by 2 to simplify, leading to \( x^{2} = 25 \). Finally, take the square root of both sides to find the solutions: \( x = 5 \) or \( x = -5 \). So, the final answers are \( x = 5 \) and \( x = -5 \). Quadratic equations like this one pop up everywhere, from calculating profits in business to determining the trajectory of a rocket! Understanding how to solve them not only sharpens mathematical skills but also opens the door to real-world applications, such as physics problem-solving or engineering design challenges. It's all about finding those x’s—so channel your inner detective!