Final answer:
The values of q that solve the quadratic equation 3.5q² − 8.6q − 3.2 = 0 can be found using the quadratic formula. By substituting a = 3.5, b = − 8.6, and c = − 3.2 into the formula, two possible solutions for q are determined.
Step-by-step explanation:
The equation given is 3.5q² − 8.6q − 3.2 = 0, which is a quadratic equation of the form aq² + bq + c = 0. To find the two values of q that satisfy the equation, we can use the quadratic formula:
q = −b ± √(b² − 4ac) / (2a)
In our case, a = 3.5, b = − 8.6,, and c = − 3.2. Substituting these values into the quadratic formula gives us:
q = −(− 8.6) ± √((− 8.6)² − 4(3.5)(− 3.2)) / (2 × 3.5)
By calculating the values under the square root and carrying out the arithmetic, we find the two possible solutions for q.