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Solve using the quadratic formula.\newlinev2+6v+8=0v^2 + 6v + 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = _____ or v=v = _____

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Q. Solve using the quadratic formula.\newlinev2+6v+8=0v^2 + 6v + 8 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinev=v = _____ or v=v = _____
  1. Write Quadratic Formula: Write down the quadratic formula.\newlineThe quadratic formula is used to solve equations of the form av2+bv+c=0av^2 + bv + c = 0. The formula is:\newlinev=−b±b2−4ac2av = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\newlineIn our equation, a=1a = 1, b=6b = 6, and c=8c = 8.
  2. Substitute Values: Substitute the values of aa, bb, and cc into the quadratic formula.v=−(6)±(6)2−4(1)(8)2(1)v = \frac{{-(6) \pm \sqrt{{(6)^2 - 4(1)(8)}}}}{{2(1)}}v=−6±36−322v = \frac{{-6 \pm \sqrt{36 - 32}}}{{2}}v=−6±42v = \frac{{-6 \pm \sqrt{4}}}{{2}}
  3. Simplify and Solve: Simplify under the square root and the fraction.\newlinev=−6±22v = \frac{{-6 \pm 2}}{{2}}\newlineThis gives us two solutions when we consider the ±\pm sign.
  4. First Solution: Solve for the first solution using the positive square root.\newlinev=(−6+2)/2v = (-6 + 2) / 2\newlinev=−4/2v = -4 / 2\newlinev=−2v = -2
  5. Second Solution: Solve for the second solution using the negative square root.\newlinev=(−6−2)/2v = (-6 - 2) / 2\newlinev=−8/2v = -8 / 2\newlinev=−4v = -4

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