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Solve using the quadratic formula.\newline2q2+4q+2=02q^2 + 4q + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____

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Q. Solve using the quadratic formula.\newline2q2+4q+2=02q^2 + 4q + 2 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineq=q = _____ or q=q = _____
  1. Quadratic Formula Definition: The quadratic formula is given by q=−b±b2−4ac2aq = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. In this case, a=2a = 2, b=4b = 4, 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 42−4(2)(2)4^2 - 4(2)(2).
  3. Discriminant Result: Perform the calculation: 16−16=016 - 16 = 0. The discriminant is 00, which means there will be one real solution (since the discriminant is not negative, there is no math error).
  4. Apply Quadratic Formula: Now, apply the quadratic formula with the calculated discriminant. Since the discriminant is 00, the formula simplifies to q=−b/(2a)q = -b / (2a). So, q=−4/(2×2)q = -4 / (2 \times 2).
  5. Final Solution: Perform the division: q=−4/4=−1q = -4 / 4 = -1. This is the only solution since the discriminant was 00.

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