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Solve using the quadratic formula.\newline2p2+8p+8=02p^2 + 8p + 8 = 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+8=02p^2 + 8p + 8 = 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. Quadratic Formula: The quadratic formula is given by p=−b±b2−4ac2ap = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the terms in the quadratic equation ap2+bp+c=0ap^2 + bp + c = 0. In this case, a=2a = 2, b=8b = 8, and c=8c = 8.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is 82−4(2)(8)8^2 - 4(2)(8).
  3. Discriminant Calculation: Perform the calculation: 64−64=064 - 64 = 0.
  4. Apply Quadratic Formula: Since the discriminant is 00, there is only one real solution to the equation. Now, apply the quadratic formula with the discriminant: p=−8±02×2p = \frac{{-8 \pm \sqrt{0}}}{{2 \times 2}}.
  5. Simplify Expression: Simplify the expression: p=−8±04p = \frac{{-8 \pm 0}}{{4}}.
  6. Divide to Find Solution: Since adding or subtracting 00 does not change the value, we have p=−84p = -\frac{8}{4}.
  7. Divide to Find Solution: Since adding or subtracting 00 does not change the value, we have p=−8/4p = -8 / 4. Divide −8-8 by 44 to get the solution: p=−2p = -2.

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