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Solve for hh.\newlineh2−11h+18=0h^2 - 11h + 18 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh = ____

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Solve a quadratic equation by factoringright chevron icon

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Q. Solve for hh.\newlineh2−11h+18=0h^2 - 11h + 18 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh = ____
  1. Identify quadratic equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is h2−11h+18=0h^2 - 11h + 18 = 0. We need to find two numbers that multiply to 1818 and add up to −11-11.
  2. Find multiplying numbers: Find two numbers that multiply to 1818 and add up to −11-11. The numbers −2-2 and −9-9 multiply to 1818 (−2×−9=18-2 \times -9 = 18) and add up to −11-11 (−2+−9=−11-2 + -9 = -11).
  3. Rewrite using numbers: Rewrite the quadratic equation by splitting the middle term using the numbers found in Step 22.\newlineh2−2h−9h+18=0h^2 - 2h - 9h + 18 = 0
  4. Factor by grouping: Factor by grouping.\newlineGroup the terms to factor by common terms:\newline(h2−2h)−(9h−18)=0 (h^2 - 2h) - (9h - 18) = 0 \newlineFactor out an h h from the first group and a −9 -9 from the second group:\newlineh(h−2)−9(h−2)=0 h(h - 2) - 9(h - 2) = 0
  5. Factor out common factor: Factor out the common binomial factor.\newline(h−2)(h−9)=0(h - 2)(h - 9) = 0
  6. Solve for hh: Solve for hh by setting each factor equal to zero.h−2=0h - 2 = 0 or h−9=0h - 9 = 0
  7. Final solutions: Solve each equation for hh.\newlineFor h−2=0h - 2 = 0, add 22 to both sides to get h=2h = 2.\newlineFor h−9=0h - 9 = 0, add 99 to both sides to get h=9h = 9.

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