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Solve for x. Enter the solutions from least to greatest. {:[x^(2)+9x+18=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2+9x+18=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+9 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+9x+18=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+9 x+18=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineWe have the quadratic equation x2+9x+18=0x^2 + 9x + 18 = 0. We need to find two numbers that multiply to 1818 and add up to 99.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineThe two numbers that multiply to 1818 and add up to 99 are 33 and 66, since 3×6=183 \times 6 = 18 and 3+6=93 + 6 = 9.\newlineSo we can write the equation as (x+3)(x+6)=0(x + 3)(x + 6) = 0.
  3. Solve for x using zero product property: Solve for x using the zero product property.\newlineIf (x+3)(x+6)=0(x + 3)(x + 6) = 0, then either x+3=0x + 3 = 0 or x+6=0x + 6 = 0.
  4. Solve the first equation: Solve the first equation x+3=0x + 3 = 0.\newlineSubtract 33 from both sides to get x=−3x = -3.
  5. Solve the second equation: Solve the second equation x+6=0x + 6 = 0.\newlineSubtract 66 from both sides to get x=−6x = -6.
  6. Write the solutions in ascending order: Write the solutions in ascending order.\newlineThe solutions are x=−6x = -6 and x=−3x = -3, with −6-6 being the lesser value and −3-3 being the greater value.

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