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Solve for x. Enter the solutions from least to greatest. {:[(x-7)^(2)-25=0],[" lesser "x= _____],[" greater "x=_____]:}

Solve for x x . Enter the solutions from least to greatest.\newline(x−7)2−25=0 lesser x=_____ greater x=_____\begin{array}{l}(x-7)^{2}-25=0 \\\text { lesser } x= \_\_\_\_\_ \\\text { greater } x=\_\_\_\_\_ \end{array}

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One-step inequalities: word problemsright chevron icon

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Q. Solve for x x . Enter the solutions from least to greatest.\newline(x−7)2−25=0 lesser x=_____ greater x=_____\begin{array}{l}(x-7)^{2}-25=0 \\\text { lesser } x= \_\_\_\_\_ \\\text { greater } x=\_\_\_\_\_ \end{array}
  1. Recognize Difference of Squares: Simplify the equation (x−7)2−25=0(x-7)^2 - 25 = 0 by recognizing that it is a difference of squares.(x−7)2−25(x-7)^2 - 25 can be factored into ((x−7)+5)((x−7)−5)((x-7) + 5)((x-7) - 5).So, (x−7)2−25=((x−7)+5)((x−7)−5)=0(x-7)^2 - 25 = ((x-7) + 5)((x-7) - 5) = 0.
  2. Set Factors Equal to Zero: Set each factor equal to zero to find the values of xx.\newlineFirst factor: (x−7)+5=0(x-7) + 5 = 0 which simplifies to x−2=0x - 2 = 0.\newlineSecond factor: (x−7)−5=0(x-7) - 5 = 0 which simplifies to x−12=0x - 12 = 0.
  3. Solve for x: Solve each equation for x.\newlineFor the first factor: x−2=0x - 2 = 0 gives x=2x = 2.\newlineFor the second factor: x−12=0x - 12 = 0 gives x=12x = 12.
  4. List Solutions: List the solutions from least to greatest.\newlineThe lesser xx is x=2x = 2.\newlineThe greater xx is x=12x = 12.

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