Questions: Solve the following quadratic equation using the quadratic formula. -16 y^2 + 8 y - 1 = 0

Solution Steps

The given quadratic equation is

\[ -16 y^{2} + 8 y - 1 = 0 \]

To solve the quadratic equation, we can use the quadratic formula:

\[ y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

where \( a = -16 \), \( b = 8 \), and \( c = -1 \).

First, we calculate the discriminant \( D \):

\[ D = b^2 - 4ac = 8^2 - 4(-16)(-1) = 64 - 64 = 0 \]

Since the discriminant is zero, there is exactly one real solution.

Now, substituting the values into the quadratic formula:

\[ y = \frac{-8 \pm \sqrt{0}}{2 \cdot -16} = \frac{-8}{-32} = \frac{1}{4} \]

Final Answer