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Solve for xx. Enter the solutions from least to greatest.\newline6x2−18x−240=06x^{2}-18x-240=0\newlinelesser x=x=\newlinegreater x=x=

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Full solution

Q. Solve for xx. Enter the solutions from least to greatest.\newline6x2−18x−240=06x^{2}-18x-240=0\newlinelesser x=x=\newlinegreater x=x=
  1. Simplify Equation: Simplify the equation by dividing all terms by 66 to make calculations easier. \newline6x2−18x−240=06x^2 - 18x - 240 = 0 \newline⇒x2−3x−40=0\Rightarrow x^2 - 3x - 40 = 0
  2. Factorize Quadratic: Factorize the quadratic equation x2−3x−40x^2 - 3x - 40.\newlineLooking for two numbers that multiply to −40-40 and add to −3-3. These numbers are −8-8 and 55.\newline=> (x−8)(x+5)=0(x - 8)(x + 5) = 0
  3. Solve for x: Solve each factor set to zero to find the values of xx.x−8=0⇒x=8x - 8 = 0 \Rightarrow x = 8x+5=0⇒x=−5x + 5 = 0 \Rightarrow x = -5

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