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Solve using the quadratic formula.\newline6v2+8v+2=06v^2 + 8v + 2 = 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.\newline6v2+8v+2=06v^2 + 8v + 2 = 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 values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 6v2+8v+2=06v^2 + 8v + 2 = 0. Compare 6v2+8v+2=06v^2 + 8v + 2 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0. a=6a = 6 bb00 bb11
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula v=b±b24ac2av = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=6a = 6, b=8b = 8, and c=2c = 2 into the quadratic formula. v=(8)±(8)246226v = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot6\cdot2}}{2\cdot6}
  3. Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant.\newline(8)2462\sqrt{(8)^2 - 4\cdot 6\cdot 2}\newline= 6448\sqrt{64 - 48}\newline= 16\sqrt{16}
  4. Continue simplifying formula: Continue simplifying the quadratic formula with the calculated discriminant. \newlinev=8±1626v = \frac{-8 \pm \sqrt{16}}{2\cdot6}\newlinev=8±412v = \frac{-8 \pm 4}{12}
  5. Calculate possible solutions: Calculate the two possible solutions for vv.v=(8+4)/12v = (-8 + 4) / 12 or v=(84)/12v = (-8 - 4) / 12v=4/12v = -4 / 12 or v=12/12v = -12 / 12Simplify the fractions.v=1/3v = -1/3 or v=1v = -1
  6. Check for simplification or rounding: Check if the solutions can be simplified further or need to be rounded.\newlineThe solutions 13-\frac{1}{3} and 1-1 are already in their simplest form and do not need to be rounded since they are exact values.

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