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Solve using the quadratic formula.\newline9v2+7v+1=09v^2 + 7v + 1 = 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.\newline9v2+7v+1=09v^2 + 7v + 1 = 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. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form av2+bv+c=0av^2 + bv + c = 0. For the equation 9v2+7v+1=09v^2 + 7v + 1 = 0, the coefficients are:\newlinea = 99\newlineb = 77\newlinec = 11
  2. Write formula: Write down the quadratic formula.\newlineThe quadratic formula is given by v=b±b24ac2av = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.\newlineSubstitute a=9a = 9, b=7b = 7, and c=1c = 1 into the quadratic formula to find the values of vv.\newlinev=7±7249129v = \frac{-7 \pm \sqrt{7^2 - 4\cdot9\cdot1}}{2\cdot9}
  4. Calculate discriminant: Calculate the discriminant (the part under the square root). The discriminant is b24acb^2 - 4ac. Discriminant = 724×9×17^2 - 4\times9\times1 Discriminant = 493649 - 36 Discriminant = 1313
  5. Calculate solutions: Calculate the two possible solutions for vv using the discriminant.v=7±1318v = \frac{{-7 \pm \sqrt{13}}}{{18}}
  6. Simplify and round: Simplify the solutions and round to the nearest hundredth if necessary.\newlineFirst solution:\newlinev=7+1318v = \frac{-7 + \sqrt{13}}{18}\newlinev7+3.6118v \approx \frac{-7 + 3.61}{18}\newlinev3.3918v \approx \frac{-3.39}{18}\newlinev0.19v \approx -0.19\newlineSecond solution:\newlinev=71318v = \frac{-7 - \sqrt{13}}{18}\newlinev73.6118v \approx \frac{-7 - 3.61}{18}\newlinev10.6118v \approx \frac{-10.61}{18}\newlinev0.59v \approx -0.59

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