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Solve for v v .\newlinev2+8v+12=0 v^2+8v+12=0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinev= v=_____

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Q. Solve for v v .\newlinev2+8v+12=0 v^2+8v+12=0\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlinev= v=_____
  1. Identify the quadratic equation: Identify the quadratic equation to be solved.\newlineWe are given the quadratic equation v2+8v+12=0v^2 + 8v + 12 = 0. We need to find the values of vv that satisfy this equation.
  2. Factor the quadratic equation: Factor the quadratic equation.\newlineTo factor the equation, we need to find two numbers that multiply to give the constant term 1212 and add up to give the coefficient of the middle term 88. The numbers that satisfy these conditions are 22 and 66, since 2×6=122 \times 6 = 12 and 2+6=82 + 6 = 8.
  3. Write the equation in factored form: Write the equation in factored form.\newlineUsing the numbers found in Step 22, we can write the equation as (v+2)(v+6)=0(v + 2)(v + 6) = 0.
  4. Solve for vv using the zero product property: Solve for vv using the zero product property.\newlineThe zero product property states that if a product of two factors is zero, then at least one of the factors must be zero. Therefore, we set each factor equal to zero and solve for vv:\newlinev+2=0v + 2 = 0 and v+6=0v + 6 = 0.
  5. Solve the first equation: Solve the first equation v+2=0v + 2 = 0.\newlineSubtract 22 from both sides to isolate vv:\newlinev+2−2=0−2v + 2 - 2 = 0 - 2\newlinev=−2v = -2
  6. Solve the second equation: Solve the second equation v+6=0v + 6 = 0.\newlineSubtract 66 from both sides to isolate vv:\newlinev+6−6=0−6v + 6 - 6 = 0 - 6\newlinev=−6v = -6

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