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Solve using the quadratic formula.\newline8s2+8s+2=08s^2 + 8s + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____

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Q. Solve using the quadratic formula.\newline8s2+8s+2=08s^2 + 8s + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlines=s = _____ or s=s = _____
  1. Quadratic Formula Definition: The quadratic formula is given by s=−b±b2−4ac2as = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the terms in the quadratic equation as2+bs+c=0as^2 + bs + c = 0. For the equation 8s2+8s+2=08s^2 + 8s + 2 = 0, a=8a = 8, b=8b = 8, and c=2c = 2.
  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(8)(2)(8)^2 - 4(8)(2).
  3. Find Discriminant Value: Perform the calculation: (8)2−4(8)(2)=64−64=0(8)^2 - 4(8)(2) = 64 - 64 = 0.
  4. Single Real Solution: Since the discriminant is 00, there is only one real solution to the equation, and it is not necessary to consider the ±\pm in the quadratic formula. We can proceed with s=−b/(2a)s = -b / (2a).
  5. Substitute Values: Substitute the values of aa and bb into the formula: s=−8(2×8)s = -\frac{8}{(2 \times 8)}.
  6. Perform Calculation: Perform the calculation: s=−816=−12s = \frac{-8}{16} = -\frac{1}{2}.
  7. Final Solution: The solution to the equation 8s2+8s+2=08s^2 + 8s + 2 = 0 is s=−12s = -\frac{1}{2}. Since the discriminant was 00, this is the only solution.

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