Solve this quadratic equation. Be sure to give \( 4 x^{2}-5=31 \)

To solve the equation \( 4x^{2}-5=31 \), start by adding 5 to both sides, yielding \( 4x^{2} = 36 \). Next, divide each side by 4 to isolate \( x^{2} \), resulting in \( x^{2} = 9 \). Finally, take the square root of both sides, leading to \( x = 3 \) or \( x = -3 \). So, the solutions are \( x = 3 \) and \( x = -3 \). For anyone diving into quadratic equations, it’s helpful to remember that they can often be solved using various methods like factoring, completing the square, or the quadratic formula. Each technique has its charm—factoring is like a puzzle, while the quadratic formula provides a reliable fail-safe solution for all cases! If you’re keen on more mathematical adventures, there’s a wealth of interactive websites and apps that can make solving equations feel like a game. Explore platforms that offer step-by-step solutions, quizzes, and challenges to sharpen your math skills while having a blast!