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Solve using the quadratic formula.\newline5j2+8j−7=05j^2 + 8j - 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+8j−7=05j^2 + 8j - 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 values of aa, bb, and cc in the quadratic equation 5j2+8j−7=05j^2 + 8j - 7 = 0.\newlineBy comparing 5j2+8j−7=05j^2 + 8j - 7 = 0 with the standard form ax2+bx+c=0ax^2 + bx + c = 0, we find:\newlinea=5a = 5\newlineb=8b = 8\newlinec=−7c = -7
  2. Substitute into formula: Substitute the values of aa, bb, and cc into the quadratic formula j=−b±b2−4ac2aj = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=5a = 5, b=8b = 8, and c=−7c = -7 into the quadratic formula. j=−(8)±(8)2−4⋅5⋅(−7)2⋅5j = \frac{-(8) \pm \sqrt{(8)^2 - 4\cdot 5\cdot (-7)}}{2\cdot 5}
  3. Calculate discriminant: Simplify the expression under the square root and calculate the discriminant. (8)2−4⋅5⋅(−7)\sqrt{(8)^2 - 4\cdot 5\cdot (-7)} = 64+140\sqrt{64 + 140} = 204\sqrt{204}
  4. Simplify formula: Simplify the quadratic formula with the calculated discriminant.\newlinej=−8±2042⋅5j = \frac{-8 \pm \sqrt{204}}{2 \cdot 5}\newlinej=−8±20410j = \frac{-8 \pm \sqrt{204}}{10}
  5. Calculate solutions: Calculate the two possible solutions for jj.\newlineFirst solution:\newlinej=−8+20410j = \frac{{-8 + \sqrt{204}}}{{10}}\newlineSecond solution:\newlinej=−8−20410j = \frac{{-8 - \sqrt{204}}}{{10}}
  6. Round to nearest hundredth: Round the values of jj to the nearest hundredth, if required.\newlineFirst solution:\newlinej≈(−8+14.28)/10j \approx (-8 + 14.28) / 10\newlinej≈6.28/10j \approx 6.28 / 10\newlinej≈0.63j \approx 0.63\newlineSecond solution:\newlinej≈(−8−14.28)/10j \approx (-8 - 14.28) / 10\newlinej≈−22.28/10j \approx -22.28 / 10\newlinej≈−2.23j \approx -2.23

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