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Solve using the quadratic formula.\newlinej2−2j−9=0j^2 - 2j - 9 = 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.\newlinej2−2j−9=0j^2 - 2j - 9 = 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 values: Identify the values of aa, bb, and cc in the quadratic equation j2−2j−9=0j^2 − 2j − 9 = 0. The quadratic equation is in the form aj2+bj+c=0aj^2 + bj + c = 0. Comparing this with our equation, we get: a=1a = 1 b=−2b = -2 c=−9c = -9
  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=1a = 1, b=−2b = -2, and c=−9c = -9 into the quadratic formula. j=−(−2)±(−2)2−4⋅1⋅(−9)2⋅1j = \frac{-(-2) \pm \sqrt{(-2)^2 - 4\cdot1\cdot(-9)}}{2\cdot1} j=2±4+362j = \frac{2 \pm \sqrt{4 + 36}}{2}
  3. Simplify and solve: Simplify the expression under the square root and solve for jj.4+36=40\sqrt{4 + 36} = \sqrt{40}.So, j=2±402j = \frac{2 \pm \sqrt{40}}{2}
  4. Simplify 40\sqrt{40}: Simplify 40\sqrt{40} and continue solving for jj.\newline40\sqrt{40} can be simplified to 2102\sqrt{10} because 40=4×1040 = 4\times10 and 4=2\sqrt{4} = 2.\newlineSo, j=2±2102j = \frac{2 \pm 2\sqrt{10}}{2}
  5. Divide and simplify: Simplify the equation by dividing both terms in the numerator by 22.j=(12±102)j = \left(\frac{1}{2} \pm \frac{\sqrt{10}}{2}\right)
  6. Calculate solutions: Calculate the two possible solutions for jj.j=1+10j = 1 + \sqrt{10} or j=1−10j = 1 - \sqrt{10}To round to the nearest hundredth, we need to approximate 10\sqrt{10} which is about 3.163.16.j≈1+3.16j \approx 1 + 3.16 or j≈1−3.16j \approx 1 - 3.16j≈4.16j \approx 4.16 or j≈−2.16j \approx -2.16

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