solve for (x): First, let’s find the discriminant ((b^2 - 4ac)) to determine the nature of the solutions: Coefficient of (x^2): (a = -1) Coefficient of (x): (b = -1) Constant term: (c = 12) Discriminant: (\Delta = b^2 - 4ac) [ \Delta = (-1)^2 - 4(-1)(12) = 1 + 48 = 49 ] Since (\Delta > 0), we have two distinct real solutions. Next, use the quadratic formula to find the values of (x): [ x = \frac{-b \pm \sqrt{\Delta}}{2a} ] [ x_1 = \frac{-(-1) + \sqrt{49}}{2(-1)} = \frac{1 + 7}{-2} = -4 ] [ x_2 = \frac{-(-1) - \sqrt{49}}{2(-1)} = \frac{1 - 7}{-2} = 3 ] Now let’s analyze the solutions: Solution 1 (x = -4): This solution is nonviable because the number of days cannot be negative. It doesn’t make sense for the friends to earn the same profit before they even start washing cars. Solution 2 (x = 3): This solution is viable. After 3 days, both friends will earn the same profit.