x^3-11x^2+18x=0 x= square square square

To solve the equation \( x^3 - 11x^2 + 18x = 0 \), we can factor out the common term \( x \):<br /><br />\[<br />x(x^2 - 11x + 18) = 0<br />\]<br /><br />This gives us two factors:<br /><br />1. \( x = 0 \)<br />2. \( x^2 - 11x + 18 = 0 \)<br /><br />Next, we need to solve the quadratic equation \( x^2 - 11x + 18 = 0 \). We can do this by factoring the quadratic expression. We look for two numbers that multiply to 18 and add up to -11. These numbers are -2 and -9.<br /><br />So, we can factor the quadratic as follows:<br /><br />\[<br />x^2 - 11x + 18 = (x - 2)(x - 9)<br />\]<br /><br />Setting each factor equal to zero gives us the solutions:<br /><br />\[<br />x - 2 = 0 \quad \text{or} \quad x - 9 = 0<br />\]<br /><br />Thus,<br /><br />\[<br />x = 2 \quad \text{or} \quad x = 9<br />\]<br /><br />Combining all the solutions, we have:<br /><br />\[<br />x = 0, \quad x = 2, \quad x = 9<br />\]<br /><br />Therefore, the solutions to the equation \( x^3 - 11x^2 + 18x = 0 \) are:<br /><br />\[<br />\boxed{0}, \boxed{2}, \boxed{9}<br />\]