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Solve using the quadratic formula.\newline2p2−8p−5=02p^2 - 8p - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinep=p = _____ or p=p = _____

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Q. Solve using the quadratic formula.\newline2p2−8p−5=02p^2 - 8p - 5 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlinep=p = _____ or p=p = _____
  1. Identify coefficients: Identify the coefficients aa, bb, and cc in the quadratic equation 2p2−8p−5=02p^2 − 8p − 5 = 0.a=2a = 2, b=−8b = -8, c=−5c = -5
  2. Write quadratic formula: Write down the quadratic formula: p=−b±b2−4ac2ap = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.
  3. Substitute values: Substitute the values of aa, bb, and cc into the quadratic formula.p=−(−8)±(−8)2−4⋅2⋅(−5)2⋅2p = \frac{-(-8) \pm \sqrt{(-8)^2 - 4 \cdot 2 \cdot (-5)}}{2 \cdot 2}
  4. Calculate discriminant: Simplify the equation by calculating the discriminant b2−4acb^2 - 4ac.\newlineDiscriminant = (−8)2−4⋅2⋅(−5)=64+40=104(-8)^2 - 4\cdot 2\cdot (-5) = 64 + 40 = 104
  5. Insert discriminant: Insert the discriminant back into the quadratic formula. p=8±1044p = \frac{8 \pm \sqrt{104}}{4}
  6. Simplify square root: Simplify the square root of the discriminant if possible. 104\sqrt{104} cannot be simplified to an integer, so we keep it as is.
  7. Calculate possible solutions: Calculate the two possible solutions for pp.p=8+1044p = \frac{8 + \sqrt{104}}{4} or p=8−1044p = \frac{8 - \sqrt{104}}{4}
  8. Round values: Round the values of pp to the nearest hundredth, if required.p≈(8+10.20)/4p \approx (8 + 10.20) / 4 or p≈(8−10.20)/4p \approx (8 - 10.20) / 4p≈18.20/4p \approx 18.20 / 4 or p≈−2.20/4p \approx -2.20 / 4p≈4.55p \approx 4.55 or p≈−0.55p \approx -0.55

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