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Solve for ww. \newlinew2+6w+5=0w^2 + 6w + 5 = 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+6w+5=0w^2 + 6w + 5 = 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 Equation: Identify the quadratic equation to be solved.\newlineWe have the quadratic equation w2+6w+5=0w^2 + 6w + 5 = 0.
  2. Factor Equation: Factor the quadratic equation.\newlineWe need to find two numbers that multiply to 55 (the constant term) and add up to 66 (the coefficient of the linear term ww). The numbers 11 and 55 satisfy these conditions because 1×5=51 \times 5 = 5 and 1+5=61 + 5 = 6.\newlineSo, we can write the quadratic equation as (w+1)(w+5)=0(w + 1)(w + 5) = 0.
  3. Solve for ww: Solve for ww using the factored form.\newlineSet each factor equal to zero and solve for ww.\newlineFirst, w+1=0w + 1 = 0, which gives us w=−1w = -1.\newlineSecond, w+5=0w + 5 = 0, which gives us w=−5w = -5.
  4. Write Solutions: Write the solutions for ww. The solutions for the equation w2+6w+5=0w^2 + 6w + 5 = 0 are w=−1w = -1 and w=−5w = -5.

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