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Solve for uu. \newlineu2−17u−18=0u^2 - 17u - 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. \newlineu=__u = \_\_

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Q. Solve for uu. \newlineu2−17u−18=0u^2 - 17u - 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. \newlineu=__u = \_\_
  1. Identify Quadratic Equation: Identify the quadratic equation to be solved.\newlineThe given quadratic equation is u2−17u−18=0u^2 - 17u - 18 = 0.\newlineWe need to find two numbers that multiply to −18-18 and add up to −17-17.
  2. Factor Quadratic Equation: Factor the quadratic equation.\newlineTo factor u2−17u−18=0u^2 - 17u - 18 = 0, we look for two numbers that multiply to give −18-18 and add to give −17-17. The numbers −18-18 and 11 satisfy these conditions because −18×1=−18-18 \times 1 = -18 and −18+1=−17-18 + 1 = -17.\newlineSo, we can write the equation as (u−18)(u+1)=0(u - 18)(u + 1) = 0.
  3. Solve Using Zero Product Property: Solve for uu using the zero product property.\newlineIf (u−18)(u+1)=0(u - 18)(u + 1) = 0, then either u−18=0u - 18 = 0 or u+1=0u + 1 = 0.
  4. Solve First Equation: Solve the first equation u−18=0u - 18 = 0. Add 1818 to both sides to isolate uu. u−18+18=0+18u - 18 + 18 = 0 + 18 u=18u = 18
  5. Solve Second Equation: Solve the second equation u+1=0u + 1 = 0.\newlineSubtract 11 from both sides to isolate uu.\newlineu+1−1=0−1u + 1 - 1 = 0 - 1\newlineu=−1u = -1

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