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Solve for uu. \newline38u2+39u=038u^2 + 39u = 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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Solve a quadratic equation by factoringright chevron icon

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Q. Solve for uu. \newline38u2+39u=038u^2 + 39u = 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. Factor GCF and Equate: Factor out the greatest common factor (GCF) from the equation 38u2+39u=038u^2 + 39u = 0. The GCF of 38u238u^2 and 39u39u is uu. Factor out uu from each term. u(38u+39)=0u(38u + 39) = 0
  2. Solve for u: Set each factor equal to zero and solve for u.\newlineFirst, set uu equal to zero:\newlineu=0u = 0\newlineThis is one solution.\newlineNext, set the other factor equal to zero:\newline38u+39=038u + 39 = 0
  3. Solve 38u+39=038u + 39 = 0: Solve the equation 38u+39=038u + 39 = 0 for uu.\newlineSubtract 3939 from both sides of the equation to isolate the term with uu.\newline38u+39−39=0−3938u + 39 - 39 = 0 - 39\newline38u=−3938u = -39\newlineNow, divide both sides by 3838 to solve for uu.\newlineu=−3938u = -\frac{39}{38}
  4. Final Solutions: Write the values of uu.\newlineWe have found two solutions: u=0u = 0 and u=−3938u = -\frac{39}{38}.

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