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Solve using the quadratic formula.\newline4n2+8n+4=04n^2 + 8n + 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+8n+4=04n^2 + 8n + 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 terms in the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=4a = 4, b=8b = 8, 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 (8)2−4(4)(4)(8)^2 - 4(4)(4).
  3. Discriminant Calculation: Perform the calculation: (8)2−4(4)(4)=64−64=0(8)^2 - 4(4)(4) = 64 - 64 = 0.
  4. Simplified Formula: Since the discriminant is 00, there is only one real solution to the equation, and it is not necessary to calculate ±b2−4ac\pm \sqrt{b^2 - 4ac} because the square root of 00 is 00. So, the formula simplifies to n=−b/(2a)n = -b / (2a).
  5. Substitute Values: Substitute the values of aa and bb into the simplified formula: n=−82×4n = -\frac{8}{2 \times 4}.
  6. Final Calculation: Perform the calculation: n=−8/8=−1n = -8 / 8 = -1.

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