Question

Solve for x in the expression using the quadratic formula. 32x²+17x-8.3=0

a) x= 0.5
b) x= -1.3
c) x= 0.8
d) x= -0.7

Answer 1

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.