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Solve for x. Enter the solutions from least to greatest. {:[x^(2)-11 x+18=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2−11x+18=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-11 x+18=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.\newlinex2−11x+18=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-11 x+18=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify Equation Type: Identify the type of equation. We have a quadratic equation in the form x2−11x+18=0x^2 - 11x + 18 = 0.
  2. Factor Quadratic Equation: Factor the quadratic equation. Look for two numbers that multiply to 1818 and add up to −11-11. The numbers are −9-9 and −2-2 because −9×−2=18-9 \times -2 = 18 and −9+−2=−11-9 + -2 = -11. So, the factored form is (x−9)(x−2)=0(x - 9)(x - 2) = 0.
  3. Set Factors Equal: Set each factor equal to zero. If (x−9)(x−2)=0(x - 9)(x - 2) = 0, then either x−9=0x - 9 = 0 or x−2=0x - 2 = 0.
  4. Solve for x (11st equation): Solve for x in the first equation. Add 99 to both sides of x−9=0x - 9 = 0 to get x=9x = 9.
  5. Solve for x (22nd equation): Solve for x in the second equation. Add 22 to both sides of x−2=0x - 2 = 0 to get x=2x = 2.
  6. List Solutions: List the solutions from least to greatest. The lesser xx is 22, and the greater xx is 99.

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