Question 12 Solve for \( x: 3 x^{3}-9 x^{2}-54 x=0 \) Important: Be sure to submit in order from least to greatest! \( x= \) Blank 1 \( x= \) Blank 2 \( x=\underline{\text { Blank } 3} \)

To solve the equation \( 3x^3 - 9x^2 - 54x = 0 \), first, factor out the common term: \[ 3x(x^2 - 3x - 18) = 0 \] Now, we have \( 3x = 0 \) or \( x^2 - 3x - 18 = 0 \). From \( 3x = 0 \), we get: \[ x = 0 \] Next, for the quadratic equation \( x^2 - 3x - 18 = 0 \), use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{3 \pm \sqrt{(-3)^2 - 4(1)(-18)}}{2(1)} \] This gives: \[ x = \frac{3 \pm \sqrt{9 + 72}}{2} = \frac{3 \pm \sqrt{81}}{2} = \frac{3 \pm 9}{2} \] Calculating the two solutions: 1. \( x = \frac{12}{2} = 6 \) 2. \( x = \frac{-6}{2} = -3 \) Now, arranging the solutions from least to greatest, we have: \( x = -3, x = 0, x = 6 \) So, the answers are: \( x= -3 \) Blank 1 \( x= 0 \) Blank 2 \( x= \underline{6} \) Blank 3