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Solve for x. Enter the solutions from least to greatest. {:[6x^(2)-12 x-210=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline6x2−12x−210=0 6 x^{2}-12 x-210=0 \newlinelesser x= x= \newlinegreater x= x=

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Q. Solve for x x . Enter the solutions from least to greatest.\newline6x2−12x−210=0 6 x^{2}-12 x-210=0 \newlinelesser x= x= \newlinegreater x= x=
  1. Write Equation: Write down the given quadratic equation.\newline6x2−12x−210=06x^2 - 12x - 210 = 0\newlineWe need to find the values of xx that satisfy this equation.
  2. Factor GCF: Factor out the greatest common factor (GCF) from the quadratic equation.\newlineThe GCF of 6x26x^2, −12x-12x, and −210-210 is 66.\newline6(x2−2x−35)=06(x^2 - 2x - 35) = 0
  3. Factor Quadratic Expression: Factor the quadratic expression inside the parentheses.\newlineWe need to find two numbers that multiply to −35-35 and add up to −2-2.\newlineThe numbers −7-7 and 55 satisfy these conditions because (−7)×5=−35(-7) \times 5 = -35 and −7+5=−2-7 + 5 = -2.\newlineSo we can write the factored form as:\newline6(x−7)(x+5)=06(x - 7)(x + 5) = 0
  4. Solve for x: Set each factor equal to zero and solve for x.\newlineFirst factor: x−7=0x - 7 = 0\newlineAdding 77 to both sides gives us x=7x = 7.\newlineSecond factor: x+5=0x + 5 = 0\newlineSubtracting 55 from both sides gives us x=−5x = -5.
  5. Write Solutions: Write down the solutions in ascending order.\newlineThe lesser value of xx is −5-5, and the greater value of xx is 77.

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