Solve for \( x \) : 1.1.1 \( 2 x^{2}-5 x=0 \)

To solve the equation \( 2x^{2} - 5x = 0 \), we can factor out \( x \) from the equation: \[ x(2x - 5) = 0 \] This gives us two potential solutions: \( x = 0 \) and \( 2x - 5 = 0 \). Solving the second equation for \( x \) gives: \[ 2x = 5 \] \[ x = \frac{5}{2} \] Thus, the solutions are \( x = 0 \) and \( x = \frac{5}{2} \). The equation represents a quadratic in standard form, and if you ever find yourself needing to solve it, remember that factoring is often a quick route—especially with two terms! When setting each factor to zero, it’s like opening a neat little treasure chest of solutions! Enjoy the treasure hunt next time you see a quadratic!