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Solve using the quadratic formula.\newline4n2+9n+5=04n^2 + 9n + 5 = 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+5=04n^2 + 9n + 5 = 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. Write Quadratic Formula: Write down the quadratic formula.\newlineThe quadratic formula is used to solve for the roots of a quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. The formula is given by:\newlinen=−b±b2−4ac2an = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
  2. Identify Coefficients: Identify the coefficients aa, bb, and cc from the quadratic equation.\newlineFor the equation 4n2+9n+5=04n^2 + 9n + 5 = 0, the coefficients are:\newlinea=4a = 4, b=9b = 9, and c=5c = 5.
  3. Substitute into Formula: Substitute the coefficients into the quadratic formula.\newlinen=−(9)±(9)2−4(4)(5)2(4)n = \frac{{-\left(9\right) \pm \sqrt{{\left(9\right)^2 - 4\left(4\right)\left(5\right)}}}}{{2\left(4\right)}}
  4. Simplify Discriminant: Simplify the expression under the square root (the discriminant). n=−9±81−808n = \frac{{-9 \pm \sqrt{{81 - 80}}}}{8}
  5. Further Simplify: Further simplify the expression. n=−9±18n = \frac{-9 \pm \sqrt{1}}{8}
  6. Calculate Possible Values: Calculate the two possible values for nn.n=−9+18n = \frac{{-9 + 1}}{{8}} or n=−9−18n = \frac{{-9 - 1}}{{8}}n=−88n = \frac{{-8}}{{8}} or n=−108n = \frac{{-10}}{{8}}
  7. Simplify Final Solutions: Simplify the fractions to get the final solutions. \newlinen=−1n = -1 or n=−108n = -\frac{10}{8}\newlinen=−1n = -1 or n=−54n = -\frac{5}{4}

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