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Solve for uu. \newlineu2+8u+16=0u^2 + 8u + 16 = 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. \newlineu2+8u+16=0u^2 + 8u + 16 = 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 solve for uu. The given equation is u2+8u+16=0u^2 + 8u + 16 = 0. We need to find values of uu that satisfy this equation.
  2. Factorization Check: Determine if the quadratic can be factored.\newlineWe are looking for two numbers that multiply to 1616 and add up to 88.\newlineThe numbers 44 and 44 satisfy these conditions because 4×4=164 \times 4 = 16 and 4+4=84 + 4 = 8.
  3. Write Factored Form: Write the factored form of the quadratic equation.\newlineSince both numbers are 44, the equation can be written as (u+4)(u+4)=0(u + 4)(u + 4) = 0.\newlineThis is also known as a perfect square trinomial.
  4. Solve for uu: Set each factor equal to zero and solve for uu.\newlineFirst, set u+4=0u + 4 = 0.\newlineSubtract 44 from both sides to solve for uu.\newlineu+4−4=0−4u + 4 - 4 = 0 - 4\newlineu=−4u = -4
  5. Final Solution: Since both factors are the same, we only get one solution for uu. The solution is u=−4u = -4. There is no need to solve the second factor because it is identical to the first.

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