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Solve for x. Enter the solutions from least to greatest. {:[(x-10)^(2)-1=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newline(x−10)2−1=0 lesser x=□ greater x=□ \begin{array}{l} (x-10)^{2}-1=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.\newline(x−10)2−1=0 lesser x=□ greater x=□ \begin{array}{l} (x-10)^{2}-1=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify the equation: Write down the given equation and identify it as a quadratic equation in the form of (a−b)2=c(a-b)^2 = c.\newlineGiven equation: (x−10)2−1=0(x-10)^2 - 1 = 0\newlineThis is a quadratic equation because it involves the square of a binomial.
  2. Isolate the squared term: Add 11 to both sides of the equation to isolate the squared term.\newline(x−10)2−1+1=0+1(x-10)^2 - 1 + 1 = 0 + 1\newline(x−10)2=1(x-10)^2 = 1
  3. Solve for x−10x-10: Take the square root of both sides of the equation to solve for x−10x-10.(x−10)2=±1\sqrt{(x-10)^2} = \pm\sqrt{1}x−10=±1x-10 = \pm1
  4. Solve for x: Solve for x by adding 1010 to both sides of the equation for both the positive and negative cases.\newlineFor the positive case:\newlinex−10+10=1+10x - 10 + 10 = 1 + 10\newlinex=11x = 11\newlineFor the negative case:\newlinex−10+10=−1+10x - 10 + 10 = -1 + 10\newlinex=9x = 9
  5. List the solutions: List the solutions in ascending order.\newlineThe lesser x=9x = 9\newlineThe greater x=11x = 11

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