Solve. \( 2 x^{2}=50 \)

To solve the equation \( 2x^{2} = 50 \), start by dividing both sides by 2 to simplify it. This gives you \( x^{2} = 25 \). Next, take the square root of both sides. Remember that both positive and negative roots should be considered, so you'll get \( x = 5 \) and \( x = -5 \). Both \( x = 5 \) and \( x = -5 \) are the solutions to the equation! Now, let’s celebrate with the fun fact that solving quadratic equations has been a cornerstone of mathematics since ancient civilizations, like the Babylonians, who approximated square roots thousands of years ago! Speaking of solving, remember that when you take the square root of both sides, it's crucial to consider both the positive and negative roots—this is a classic mistake many make! Enjoy your math adventure!