<prompt> Given the following equation, solve for x : 4x29x1 0  <response>: The given equation is a quadratic equation of the form Ax2 Bx C 0, where A4, B9, and C1. To solve this equation for x, we can use the quadratic formula, given as follows:x -B B2 - 4AC2ASubstituting the given values of A, B and C in the above formula, we get:x -9 92 - 44124x -9 81 - 168x -9 658So the two solutions of the given quadratic equation are :x -9 658 and x -9 - 658. 