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Solve for x. Enter the solutions from least to greatest. {:[x^(2)-14 x+40=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2−14x+40=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-14 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.\newlinex2−14x+40=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-14 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 x2−14x+40=0x^2 - 14x + 40 = 0. We need to find the values of xx that satisfy this equation.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 4040 (the constant term) and add up to −14-14 (the coefficient of the xx term). The numbers that satisfy these conditions are −10-10 and −4-4, since −10×−4=40-10 \times -4 = 40 and −10+−4=−14-10 + -4 = -14.\newlineSo, we can write the equation as (x−10)(x−4)=0(x - 10)(x - 4) = 0.
  3. Solve for x using zero product property: Solve for x using the zero product property.\newlineIf (x−10)(x−4)=0(x - 10)(x - 4) = 0, then either x−10=0x - 10 = 0 or x−4=0x - 4 = 0.\newlineFor x−10=0x - 10 = 0:\newlinex=10x = 10\newlineFor x−4=0x - 4 = 0:\newlinex=4x = 4\newlineThese are the two solutions to the equation.
  4. List the solutions in ascending order: List the solutions in ascending order.\newlineThe lesser value of xx is 44, and the greater value of xx is 1010.

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