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Solve using the quadratic formula.\newline2j2−8j−4=02j^2 - 8j - 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = _____ or j=j = _____

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Q. Solve using the quadratic formula.\newline2j2−8j−4=02j^2 - 8j - 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinej=j = _____ or j=j = _____
  1. Identify coefficients: Identify the coefficients of the quadratic equation.\newlineThe quadratic equation is in the form of aj2+bj+c=0a j^2 + b j + c = 0. For the equation 2j2−8j−4=02 j^2 - 8 j - 4 = 0, the coefficients are:\newlinea = 22\newlineb = −8-8\newlinec = −4-4
  2. Substitute into formula: Substitute the coefficients into the quadratic formula.\newlineThe quadratic formula is j=−b±b2−4ac2aj = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substituting the values we get:\newlinej=−(−8)±(−8)2−4⋅2⋅(−4)2⋅2j = \frac{-(-8) \pm \sqrt{(-8)^2 - 4\cdot2\cdot(-4)}}{2\cdot2}\newlinej=8±64+324j = \frac{8 \pm \sqrt{64 + 32}}{4}
  3. Simplify square root: Simplify the expression under the square root.\newlineCalculate the value inside the square root:\newline64+32=96\sqrt{64 + 32} = \sqrt{96}
  4. Simplify quadratic formula: Simplify the quadratic formula.\newlineNow we have:\newlinej=8±964j = \frac{8 \pm \sqrt{96}}{4}\newlineSince 96\sqrt{96} can be simplified to 464\sqrt{6}, we can further simplify the expression:\newlinej=8±464j = \frac{8 \pm 4\sqrt{6}}{4}\newlinej=2±6j = 2 \pm \sqrt{6}
  5. Calculate possible solutions: Calculate the two possible solutions for jj. We have two solutions based on the ±\pm sign in the formula: j=2+6j = 2 + \sqrt{6} or j=2−6j = 2 - \sqrt{6}
  6. Round to nearest hundredth: Round the values of jj to the nearest hundredth, if required.j=2+6≈2+2.45≈4.45j = 2 + \sqrt{6} \approx 2 + 2.45 \approx 4.45j=2−6≈2−2.45≈−0.45j = 2 - \sqrt{6} \approx 2 - 2.45 \approx -0.45

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