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Solve for x. Enter the solutions from least to greatest. {:[3x^(2)-33 x+54=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline3x2−33x+54=0 3 x^{2}-33 x+54=0 \newlinelesser x= x= \newlinegreater x= x=

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Q. Solve for x x . Enter the solutions from least to greatest.\newline3x2−33x+54=0 3 x^{2}-33 x+54=0 \newlinelesser x= x= \newlinegreater x= x=
  1. Identify the quadratic equation: Identify the quadratic equation and its coefficients.\newlineThe quadratic equation is 3x2−33x+54=03x^2 - 33x + 54 = 0, where the coefficients are A=3A = 3, B=−33B = -33, and C=54C = 54.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to A⋅CA \cdot C (3⋅54)(3 \cdot 54) and add up to BB (−33)(-33).\newlineThe numbers that satisfy these conditions are −9-9 and −24-24 because −9⋅−24=216-9 \cdot -24 = 216 and −9+−24=−33-9 + -24 = -33.
  3. Rewrite the quadratic equation: Rewrite the quadratic equation using the numbers found in Step 22.\newline3x2−9x−24x+54=03x^2 - 9x - 24x + 54 = 0\newlineGroup the terms: (3x2−9x)−(24x−54)=0(3x^2 - 9x) - (24x - 54) = 0
  4. Factor by grouping: Factor by grouping.\newlineFactor out the common terms from each group:\newline3x(x−3)−18(x−3)=03x(x - 3) - 18(x - 3) = 0\newlineNow factor out the common binomial factor (x−3)(x - 3):\newline(3x−18)(x−3)=0(3x - 18)(x - 3) = 0
  5. Simplify the factored equation: Simplify the factored equation.\newlineDivide the first term by 33 to simplify:\newline(x−6)(x−3)=0(x - 6)(x - 3) = 0
  6. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−6=0x - 6 = 0 or x−3=0x - 3 = 0\newlineSolve each equation:\newlinex=6x = 6 or x=3x = 3

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