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Solve using the quadratic formula.\newline5n2+9n+4=05n^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.\newline5n2+9n+4=05n^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. Quadratic Formula: The quadratic formula is given by n=−b±b2−4ac2an = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=5a = 5, b=9b = 9, and c=4c = 4.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. For our equation, the discriminant is 92−4(5)(4)9^2 - 4(5)(4).
  3. Discriminant Calculation: Perform the calculation: 92−4(5)(4)=81−80=19^2 - 4(5)(4) = 81 - 80 = 1.
  4. Apply Quadratic Formula: Since the discriminant is positive, there will be two real solutions. Now, apply the quadratic formula with the calculated discriminant.\newlinen=−9±12×5n = \frac{-9 \pm \sqrt{1}}{2 \times 5}
  5. Simplify Equation: Simplify the square root of the discriminant and the equation: n=−9±110n = \frac{-9 \pm 1}{10}.
  6. Find Solutions: Find the two solutions by performing the addition and subtraction:\newlineFirst solution: n=(−9+1)/10=−8/10=−4/5n = (-9 + 1) / 10 = -8 / 10 = -4/5\newlineSecond solution: n=(−9−1)/10=−10/10=−1n = (-9 - 1) / 10 = -10 / 10 = -1
  7. Simplify Fractions: Simplify the fractions to their simplest form if necessary. The first solution is already in simplest form, and the second solution is an integer.

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