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Solve for x. Enter the solutions from least to greatest. {:[x^(2)-8x+7=0],[" lesser "x=◻],[" greater "x=◻]:}

Solve for x x . Enter the solutions from least to greatest.\newlinex2−8x+7=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-8 x+7=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.\newlinex2−8x+7=0 lesser x=□ greater x=□ \begin{array}{l} x^{2}-8 x+7=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}
  1. Identify the quadratic equation: Identify the quadratic equation and its coefficients.\newlineThe quadratic equation is x2−8x+7=0x^2 - 8x + 7 = 0, where the coefficients are A=1A = 1, B=−8B = -8, and C=7C = 7.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to give C(7)C (7) and add up to give B(−8)B (-8). The numbers that satisfy these conditions are −1-1 and −7-7 because (−1)×(−7)=7(-1) \times (-7) = 7 and (−1)+(−7)=−8(-1) + (-7) = -8.
  3. Write the factored form: Write the factored form of the equation.\newlineThe factored form of the equation is (x−1)(x−7)=0(x - 1)(x - 7) = 0.
  4. Solve for x by setting each factor equal to zero: Solve for x by setting each factor equal to zero.\newlineFirst, set the first factor equal to zero: x−1=0x - 1 = 0. Then, solve for x by adding 11 to both sides: x=1x = 1.
  5. Solve for x using the second factor: Solve for x using the second factor.\newlineSet the second factor equal to zero: x−7=0x - 7 = 0. Then, solve for x by adding 77 to both sides: x=7x = 7.
  6. Write the solutions in ascending order: Write the solutions in ascending order.\newlineThe solutions are x=1x = 1 and x=7x = 7, with 11 being the lesser value and 77 being the greater value.

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