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Solve using the quadratic formula.\newlinej2−6j+4=0j^2 - 6j + 4 = 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.\newlinej2−6j+4=0j^2 - 6j + 4 = 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 j2−6j+4=0j^2 − 6j + 4 = 0. The standard form of a quadratic equation is ax2+bx+c=0ax^2 + bx + c = 0. Comparing this with our equation, we get: a=1a = 1 b=−6b = -6 c=4c = 4
  2. Substitute values into formula: Substitute the values of aa, bb, and cc into the quadratic formula to find jj. The quadratic formula is j=−b±b2−4ac2aj = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. So we have: j=−(−6)±(−6)2−4⋅1⋅42⋅1j = \frac{-(-6) \pm \sqrt{(-6)^2 - 4\cdot1\cdot4}}{2\cdot1}
  3. Simplify expression and constants: Simplify the expression under the square root and the constants outside the square root. \newlinej=6±36−162j = \frac{6 \pm \sqrt{36 - 16}}{2}\newlinej=6±202j = \frac{6 \pm \sqrt{20}}{2}
  4. Factor and simplify square root: Simplify the square root of 2020 by factoring it into 4×54\times5 and taking the square root of 44 out of the square root.20=4×5=2×5\sqrt{20} = \sqrt{4\times5} = 2\times\sqrt{5}Now substitute this back into the equation:j=6±2×52j = \frac{6 \pm 2\times\sqrt{5}}{2}
  5. Divide terms by 22: Simplify the equation by dividing both terms in the numerator by 22.\newlinej=3±52j = \frac{3 \pm \sqrt{5}}{2}
  6. Approximate solutions: Since 5\sqrt{5} cannot be simplified to an integer or a simple fraction, we will leave it as is or round it to the nearest hundredth if necessary.\newlineThe approximate value of 5\sqrt{5} is 2.242.24.\newlineSo the approximate solutions for jj are:\newlinej≈3+2.24j \approx 3 + 2.24 or j≈3−2.24j \approx 3 - 2.24\newlinej≈5.24j \approx 5.24 or j≈0.76j \approx 0.76

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