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Solve using the quadratic formula.\newline5j2−6j−7=05j^2 - 6j - 7 = 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.\newline5j2−6j−7=05j^2 - 6j - 7 = 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 5j2−6j−7=05j^2 − 6j − 7 = 0. The quadratic equation is in the form aj2+bj+c=0aj^2 + bj + c = 0, so by comparison, we have: a=5a = 5 b=−6b = -6 c=−7c = -7
  2. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.\newlineThe quadratic formula is j=−b±b2−4ac2aj = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.\newlineSubstitute a=5a = 5, b=−6b = -6, and c=−7c = -7 into the formula to get:\newlinej=−(−6)±(−6)2−4⋅5⋅(−7)2⋅5j = \frac{-(-6) \pm \sqrt{(-6)^2 - 4\cdot5\cdot(-7)}}{2\cdot5}
  3. Simplify discriminant: Simplify the expression under the square root (the discriminant).\newlineCalculate the discriminant: (−6)2−4⋅5⋅(−7)=36+140=176(-6)^2 - 4\cdot5\cdot(-7) = 36 + 140 = 176.
  4. Continue simplifying: Continue simplifying the quadratic formula with the discriminant.\newlineNow we have:\newlinej=6±17610j = \frac{6 \pm \sqrt{176}}{10}
  5. Simplify square root: Simplify the square root, if possible.\newlineThe square root of 176176 cannot be simplified to an integer, so we leave it as 176\sqrt{176}.
  6. Calculate possible solutions: Calculate the two possible solutions for jj.j=6+17610j = \frac{6 + \sqrt{176}}{10} or j=6−17610j = \frac{6 - \sqrt{176}}{10}
  7. Round values: Round the values of jj to the nearest hundredth, if required.j≈(6+13.27)/10j \approx (6 + 13.27) / 10 or j≈(6−13.27)/10j \approx (6 - 13.27) / 10j≈19.27/10j \approx 19.27 / 10 or j≈−7.27/10j \approx -7.27 / 10j≈1.93j \approx 1.93 or j≈−0.73j \approx -0.73

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