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Solve for x. Enter the solutions from least to greatest. {:[x^(2)+x-42=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2+x−42=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+x-42=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+x−42=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}+x-42=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+x−42=0x^2 + x - 42 = 0. We need to find two numbers that multiply to −42-42 and add up to 11, which are the coefficients of the x2x^2 and xx terms, respectively.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineThe two numbers that multiply to −42-42 and add up to 11 are 77 and −6-6 because 7×(−6)=−427 \times (-6) = -42 and 7+(−6)=17 + (-6) = 1. Therefore, we can factor the quadratic equation as follows:\newlinex2+x−42=(x+7)(x−6)=0x^2 + x - 42 = (x + 7)(x - 6) = 0
  3. Solve for x: Solve for x using the zero product property.\newlineIf (x+7)(x−6)=0(x + 7)(x - 6) = 0, then either x+7=0x + 7 = 0 or x−6=0x - 6 = 0.\newlineFor x+7=0x + 7 = 0:\newlinex=−7x = -7\newlineFor x−6=0x - 6 = 0:\newlinex=6x = 6
  4. Write the solutions: Write the solutions in ascending order.\newlineThe lesser value of xx is −7-7, and the greater value of xx is 66.

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