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Solve for x. Enter the solutions from least to greatest. {:[6x^(2)-18 x-240=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline6x2−18x−240=0 6 x^{2}-18 x-240=0 \newlinelesser x= x= \newlinegreater x= x=

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Q. Solve for x x . Enter the solutions from least to greatest.\newline6x2−18x−240=0 6 x^{2}-18 x-240=0 \newlinelesser x= x= \newlinegreater x= x=
  1. Simplify the equation: 6x2−18x−240=06x^2 - 18x - 240 = 0\newlineFirst, we can simplify the equation by dividing all terms by 66 to make the numbers smaller and easier to work with.\newlinex2−3x−40=0x^2 - 3x - 40 = 0
  2. Find the multiplying and adding numbers: Find two numbers that multiply to −40-40 and add up to −3-3.\newlineThe numbers −8-8 and 55 satisfy these conditions because:\newline−8×5=−40-8 \times 5 = -40\newline−8+5=−3-8 + 5 = -3
  3. Rewrite the quadratic equation: Rewrite the quadratic equation using the numbers found in Step 22.\newlinex2−8x+5x−40=0x^2 - 8x + 5x - 40 = 0
  4. Factor by grouping: Factor by grouping.\newlineGroup the terms to factor by common terms:\newline(x2−8x)+(5x−40)=0 (x^2 - 8x) + (5x - 40) = 0 \newlineFactor out an x x from the first group and a 5 5 from the second group:\newlinex(x−8)+5(x−8)=0 x(x - 8) + 5(x - 8) = 0
  5. Factor out the common binomial factor: Factor out the common binomial factor.\newline(x−8)(x+5)=0(x - 8)(x + 5) = 0
  6. Solve for x: Solve for x by setting each factor equal to zero.\newlinex−8=0x - 8 = 0 or x+5=0x + 5 = 0\newlineSolving each equation gives us:\newlinex=8x = 8 or x=−5x = -5
  7. Write the solutions in ascending order: Write the solutions in ascending order.\newlineThe lesser value of xx is −5-5, and the greater value of xx is 88.

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