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Solve for x. Enter the solutions from least to greatest. {:[3x^(2)+36 x+81=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline3x2+36x+81=0 lesser x=□ greater x=□ \begin{array}{l} 3 x^{2}+36 x+81=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

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Q. Solve for x x . Enter the solutions from least to greatest.\newline3x2+36x+81=0 lesser x=□ greater x=□ \begin{array}{l} 3 x^{2}+36 x+81=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify Quadratic Equation: Identify the quadratic equation to solve.\newlineThe given quadratic equation is 3x2+36x+81=03x^2 + 36x + 81 = 0. We need to find the values of xx that satisfy this equation.
  2. Factor Quadratic Equation: Factor the quadratic equation, if possible.\newlineThe quadratic equation 3x2+36x+813x^2 + 36x + 81 can be factored as (3x+9)(x+9)=0(3x + 9)(x + 9) = 0, because 3x2+36x+813x^2 + 36x + 81 is a perfect square trinomial.
  3. Set Factors Equal: Set each factor equal to zero and solve for xx.\newlineFirst factor: 3x+9=03x + 9 = 0\newlineSecond factor: x+9=0x + 9 = 0\newlineFor the first factor:\newline3x+9=03x + 9 = 0\newline3x=−93x = -9\newlinex=−9/3x = -9 / 3\newlinex=−3x = -3\newlineFor the second factor:\newlinex+9=0x + 9 = 0\newlinex=−9x = -9\newlineBoth factors give us the same solution for xx.
  4. Check Solutions: Check the solutions.\newlinePlugging x=−3x = -3 into the original equation:\newline3(−3)2+36(−3)+81=03(-3)^2 + 36(-3) + 81 = 0\newline27+(−108)+81=027 + (-108) + 81 = 0\newline0=00 = 0\newlineThe solution x=−3x = -3 satisfies the original equation.

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