Answer:
Explanation:
To solve the quadratic equation 16x^2 - 8x = -1 using the quadratic formula, we need to rearrange the equation in the standard form ax^2 + bx + c = 0.
Given equation: 16x^2 - 8x = -1
We bring all terms to one side to obtain: 16x^2 - 8x + 1 = 0
Comparing this with the standard form ax^2 + bx + c = 0, we have:
a = 16
b = -8
c = 1
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Substituting the values, we get:
x = (-(-8) ± √((-8)^2 - 4 * 16 * 1)) / (2 * 16)
x = (8 ± √(64 - 64)) / 32
x = (8 ± √0) / 32
Since the discriminant (b^2 - 4ac) is zero, the quadratic equation has only one real root.
x = 8 / 32
x = 1/4
Therefore, the solution to the equation 16x^2 - 8x = -1 is x = 1/4.