How do I use the quadratic formula to solve the equation 7x² + 7 = 0, and what are the values of x?

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To solve the quadratic equation 7x² + 7 = 0, we first need to rewrite it in the standard quadratic form, which is ax² + bx + c = 0. In this case:

  • a = 7
  • b = 0
  • c = 7

Next, we can use the quadratic formula, which is:

x = (-b ± √(b² – 4ac)) / (2a)

  1. Calculate the discriminant (b² – 4ac):

    2. In our case:

    • b² = 0² = 0
    • 4ac = 4 * 7 * 7 = 196

    So, the discriminant is:

    0 – 196 = -196

  2. Since the discriminant is negative (-196), this means that there are no real solutions. However, we can find complex solutions.
  3. Next, we substitute the values of a, b, and the discriminant into the quadratic formula:

    4. x = (-0 ± √(-196)) / (2 * 7)

    Calculating further:

    √(-196) = √(196) * √(-1) = 14i

  4. Now we substitute this back into our equation:

    5. x = (0 ± 14i) / 14

    This simplifies to:

    • x = 14i / 14 = i
    • x = -14i / 14 = -i

Therefore, the solutions to the equation 7x² + 7 = 0 are:

x = i and x = -i

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