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Solve for x. Enter the solutions from least to greatest. {:[6x^(2)-30 x-84=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline6x2−30x−84=0 6 x^{2}-30 x-84=0 \newlinelesser x= x= \newlinegreater x= x=

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Q. Solve for x x . Enter the solutions from least to greatest.\newline6x2−30x−84=0 6 x^{2}-30 x-84=0 \newlinelesser x= x= \newlinegreater x= x=
  1. Factor GCF: Factor out the greatest common factor (GCF) from the quadratic equation.\newlineThe GCF of 6x26x^2, −30x-30x, and −84-84 is 66. Let's factor out 66 from each term.\newline6(x2−5x−14)=06(x^2 - 5x - 14) = 0
  2. Solve Equation: Solve the factored quadratic equation.\newlineNow we need to solve the equation x2−5x−14=0x^2 - 5x - 14 = 0 by factoring.\newlineWe look for two numbers that multiply to −14-14 and add up to −5-5. These numbers are −7-7 and 22.\newlineSo, we can write the equation as (x−7)(x+2)=0(x - 7)(x + 2) = 0.
  3. Find Values of x: Find the values of xx. For the equation (x−7)(x+2)=0(x - 7)(x + 2) = 0 to hold true, either (x−7)=0(x - 7) = 0 or (x+2)=0(x + 2) = 0. Solving for xx in each case gives us: x−7=0⇒x=7x - 7 = 0 \Rightarrow x = 7 x+2=0⇒x=−2x + 2 = 0 \Rightarrow x = -2
  4. Determine xx Values: Determine which value of xx is lesser and which is greater.\newlineComparing the two solutions, −2-2 is less than 77.\newlineSo, the lesser xx is −2-2 and the greater xx is 77.

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