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Solve for ww.\newlinew2−19w−20=0w^2 - 19w - 20 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinew=__w = \_\_

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Solve a quadratic equation by factoringright chevron icon

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Q. Solve for ww.\newlinew2−19w−20=0w^2 - 19w - 20 = 0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinew=__w = \_\_
  1. Identify Quadratic Equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is w2−19w−20=0w^2 - 19w - 20 = 0. We need to find two numbers that multiply to −20-20 and add up to −19-19.
  2. Find Multiplying Numbers: Find two numbers that multiply to −20-20 and add up to −19-19. The numbers −20-20 and 11 have a product of −20-20 and a sum of −19-19. −20×1=−20-20 \times 1 = -20 −20+1=−19-20 + 1 = -19
  3. Rewrite Using Numbers: Rewrite the quadratic equation by splitting the middle term using the numbers found in Step 22.\newlinew2−20w+w−20=0w^2 - 20w + w - 20 = 0
  4. Factor by Grouping: Factor by grouping.\newlineGroup the terms to factor out common factors.\newline(w2−20w)+(w−20)=0(w^2 - 20w) + (w - 20) = 0\newlinew(w−20)+1(w−20)=0w(w - 20) + 1(w - 20) = 0\newline(w−20)(w+1)=0(w - 20)(w + 1) = 0
  5. Solve Using Zero Product Property: Solve for ww using the zero product property.\newlineSet each factor equal to zero and solve for ww.\newlinew−20=0w - 20 = 0 or w+1=0w + 1 = 0\newlinew=20w = 20 or w=−1w = -1

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