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Solve using the quadratic formula.\newlinej2−9j−7=0j^2 - 9j - 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.\newlinej2−9j−7=0j^2 - 9j - 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 j2−9j−7=0j^2 − 9j − 7 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.
    a=1a = 1
    b=−9b = -9
    c=−7c = -7
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula, which is j=−b±b2−4ac2aj = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. \newlinej=−(−9)±(−9)2−4⋅1⋅(−7)2⋅1j = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot 1\cdot (-7)}}{2\cdot 1}
  3. Simplify expression and constants: Simplify the expression inside the square root and the constants outside the square root. \newlinej=9±81+282j = \frac{9 \pm \sqrt{81 + 28}}{2}\newlinej=9±1092j = \frac{9 \pm \sqrt{109}}{2}
  4. Calculate possible solutions: Calculate the two possible solutions for jj by adding and subtracting the square root.j=9+1092j = \frac{9 + \sqrt{109}}{2} or j=9−1092j = \frac{9 - \sqrt{109}}{2}
  5. Round values if necessary: Round the values of jj to the nearest hundredth, if necessary.j≈(9+10.44)/2j \approx (9 + 10.44) / 2 or j≈(9−10.44)/2j \approx (9 - 10.44) / 2j≈19.44/2j \approx 19.44 / 2 or j≈−1.44/2j \approx -1.44 / 2j≈9.72j \approx 9.72 or j≈−0.72j \approx -0.72

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