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Solve using the quadratic formula.\newline3j2+3j−8=03j^2 + 3j - 8 = 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.\newline3j2+3j−8=03j^2 + 3j - 8 = 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 aa, bb, and cc in the quadratic equation 3j2+3j−8=03j^2 + 3j - 8 = 0.a=3a = 3, b=3b = 3, c=−8c = -8
  2. Write quadratic formula: Write down the quadratic formula: j=−b±b2−4ac2aj = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.j=−(3)±(3)2−4(3)(−8)2(3)j = \frac{-(3) \pm \sqrt{(3)^2 - 4(3)(-8)}}{2(3)}
  4. Simplify expression: Simplify the expression under the square root (the discriminant). (3)2−4(3)(−8)=9+96=105\sqrt{(3)^2 - 4(3)(-8)} = \sqrt{9 + 96} = \sqrt{105}
  5. Simplify formula: Simplify the quadratic formula with the values. j=−3±1056j = \frac{-3 \pm \sqrt{105}}{6}
  6. Calculate solutions: Calculate the two possible solutions for jj.j=−3+1056j = \frac{{-3 + \sqrt{105}}}{{6}} or j=−3−1056j = \frac{{-3 - \sqrt{105}}}{{6}}
  7. Round values: Round the values of jj to the nearest hundredth, if required.j \approx (\-3 + 10.25) / 6 or j \approx (\-3 - 10.25) / 6j≈7.25/6j \approx 7.25 / 6 or j≈−13.25/6j \approx -13.25 / 6j≈1.21j \approx 1.21 or j≈−2.21j \approx -2.21

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