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Solve for x. Enter the solutions from least to greatest. {:[x^(2)-5x-14=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2−5x−14=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-5 x-14=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.\newlinex2−5x−14=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-5 x-14=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is x2−5x−14=0x^2 - 5x - 14 = 0. We need to find two numbers that multiply to −14-14 and add up to −5-5.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineTo factor x2−5x−14x^2 - 5x - 14, we look for two numbers that multiply to −14-14 and add to −5-5. The numbers −7-7 and 22 satisfy these conditions because −7×2=−14-7 \times 2 = -14 and −7+2=−5-7 + 2 = -5.\newlineSo, we can write the equation as (x−7)(x+2)=0(x - 7)(x + 2) = 0.
  3. Solve for x: Solve for x using the zero product property.\newlineIf (x−7)(x+2)=0(x - 7)(x + 2) = 0, then either x−7=0x - 7 = 0 or x+2=0x + 2 = 0.\newlineSolving x−7=0x - 7 = 0 gives us x=7x = 7.\newlineSolving x+2=0x + 2 = 0 gives us x=−2x = -2.
  4. Write the solutions: Write the solutions in ascending order.\newlineThe lesser value of xx is −2-2, and the greater value of xx is 77.

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