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Solve for uu. \newline7u2+13u−2=07u^2 + 13u - 2 = 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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Full solution

Q. Solve for uu. \newline7u2+13u−2=07u^2 + 13u - 2 = 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. Find Numbers: Find two numbers that multiply to a×ca \times c (7×−2=−147 \times -2 = -14) and add up to bb (1313).
  2. Apply Numbers: The numbers that work are 1414 and −1-1 because 14×−1=−1414 \times -1 = -14 and 14+(−1)=1314 + (-1) = 13.
  3. Rewrite Middle Term: Rewrite the middle term using the numbers found in Step 22: 7u2+14u−u−27u^2 + 14u - u - 2.
  4. Factor by Grouping: Factor by grouping: (7u2+14u)+(−u−2)(7u^2 + 14u) + (-u - 2).
  5. Factor Common Terms: Factor out the common terms: 7u(u+2)−1(u+2)7u(u + 2) - 1(u + 2).
  6. Factor Common Binomial: Factor out the common binomial: (7u−1)(u+2)(7u - 1)(u + 2).
  7. Set Equal to Zero: Set each factor equal to zero: 7u−1=07u - 1 = 0 and u+2=0u + 2 = 0.
  8. Solve for u: Solve for u from the first equation: 7u=17u = 1; u=17.u = \frac{1}{7}.
  9. Solve for u: Solve for u from the first equation: 7u=17u = 1; u=17u = \frac{1}{7}.Solve for u from the second equation: u=−2u = -2.

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