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Solve using the quadratic formula.\newline4n2−9n+4=04n^2 - 9n + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinen=n = _____ or n=n = _____

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Q. Solve using the quadratic formula.\newline4n2−9n+4=04n^2 - 9n + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinen=n = _____ or n=n = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 4n2−9n+4=04n^2 - 9n + 4 = 0 by comparing it to the standard form ax2+bx+c=0ax^2 + bx + c = 0.a=4a = 4, b=−9b = -9, c=4c = 4
  2. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula, n=−b±b2−4ac2an = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.n=−(−9)±(−9)2−4⋅4⋅42⋅4n = \frac{-(-9) \pm \sqrt{(-9)^2 - 4\cdot4\cdot4}}{2\cdot4}
  3. Simplify expression: Simplify the expression inside the square root and the constants outside the square root. \newlinen=9±81−648n = \frac{9 \pm \sqrt{81 - 64}}{8}\newlinen=9±178n = \frac{9 \pm \sqrt{17}}{8}
  4. Calculate solutions: Calculate the two possible solutions for nn using the simplified square root value.n=9+178n = \frac{9 + \sqrt{17}}{8} or n=9−178n = \frac{9 - \sqrt{17}}{8}
  5. Round values: If necessary, round the values of nn to the nearest hundredth.n≈(9+4.12)/8n \approx (9 + 4.12) / 8 or n≈(9−4.12)/8n \approx (9 - 4.12) / 8n≈13.12/8n \approx 13.12 / 8 or n≈4.88/8n \approx 4.88 / 8n≈1.64n \approx 1.64 or n≈0.61n \approx 0.61

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