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Solve using the quadratic formula.\newline8n26n8=08n^2 - 6n - 8 = 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.\newline8n26n8=08n^2 - 6n - 8 = 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 8n26n8=08n^2 − 6n − 8 = 0.a=8a = 8, b=6b = -6, c=8c = -8
  2. Write quadratic formula: Write down the quadratic formula: n=b±b24ac2an = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.n=(6)±(6)248(8)28n = \frac{-(-6) \pm \sqrt{(-6)^2 - 4 \cdot 8 \cdot (-8)}}{2 \cdot 8}
  4. Calculate discriminant: Simplify the equation by calculating the discriminant b24acb^2 - 4ac.\newlineDiscriminant = (6)248(8)(-6)^2 - 4\cdot8\cdot(-8) = 36+25636 + 256 = 292292
  5. Insert discriminant: Insert the value of the discriminant back into the quadratic formula. n=6±29216n = \frac{6 \pm \sqrt{292}}{16}
  6. Simplify square root: Simplify the square root of the discriminant if possible. 292\sqrt{292} cannot be simplified further as a square root of an integer.
  7. Calculate solutions: Calculate the two possible solutions for nn.n=6+29216n = \frac{6 + \sqrt{292}}{16} or n=629216n = \frac{6 - \sqrt{292}}{16}
  8. Round values: Round the values of nn to the nearest hundredth, if required.n(6+17.09)/16n \approx (6 + 17.09) / 16 or n(617.09)/16n \approx (6 - 17.09) / 16n23.09/16n \approx 23.09 / 16 or n11.09/16n \approx -11.09 / 16n1.44n \approx 1.44 or n0.69n \approx -0.69

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