Final answer:
The quadratic equation 32x² + 17x - 8.3 = 0 is solved using the quadratic formula, with the coefficients a=32, b=17, and c=-8.3. After calculating the discriminant and plugging values into the formula, we find two possible solutions for x. However, neither of these solutions match the provided options.
Step-by-step explanation:
To solve the equation 32x² + 17x - 8.3 = 0 using the quadratic formula, we first need to identify the coefficients corresponding to the terms ax² + bx + c = 0. In our equation, a is 32, b is 17, and c is -8.3.
The quadratic formula is given by:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values we get:
x = (-(17) ± √((17)² - 4(32)(-8.3))) / (2(32))
Computing the discriminant (b² - 4ac):
√((17)² - 4(32)(-8.3)) = √(289 + 1065.6)
Finding the square root of the discriminant:
√(1354.6) ≈ 36.813
Now, we calculate the two possible values for x:
- x = (-(17) + 36.813) / (64) ≈ 0.3102
- x = (-(17) - 36.813) / (64) ≈ -0.8421
However, none of the provided options match these values.