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Solve for x. Enter the solutions from least to greatest. {:[x^(2)-3x-40=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2−3x−40=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-3 x-40=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.\newlinex2−3x−40=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-3 x-40=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is x2−3x−40=0x^2 - 3x - 40 = 0. We need to find two numbers that multiply to −40-40 and add up to −3-3.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineTo factor x2−3x−40=0x^2 - 3x - 40 = 0, we look for two numbers that multiply to give −40-40 and add to give −3-3. The numbers −8-8 and 55 satisfy these conditions because −8×5=−40-8 \times 5 = -40 and −8+5=−3-8 + 5 = -3.\newlineSo, we can write the equation as (x−8)(x+5)=0(x - 8)(x + 5) = 0.
  3. Solve for x using zero product property: Solve for x using the zero product property.\newlineIf (x−8)(x+5)=0(x - 8)(x + 5) = 0, then either x−8=0x - 8 = 0 or x+5=0x + 5 = 0.
  4. Solve the first equation: Solve the first equation x−8=0x - 8 = 0.\newlineAdding 88 to both sides gives us x=8x = 8.
  5. Solve the second equation: Solve the second equation x+5=0x + 5 = 0.\newlineSubtracting 55 from both sides gives us x=−5x = -5.
  6. Write the solutions in ascending order: Write the solutions in ascending order.\newlineThe solutions are x=−5x = -5 and x=8x = 8. In ascending order, the lesser value is −5-5 and the greater value is 88.

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