Final answer:
To solve the quadratic equation 2x² + 23x - 6.1 = 0, we use the quadratic formula by substituting a = 2, b = 23, and c = -6.1, which yields solutions x ≈ 0.25925 and x ≈ -11.75925.
Step-by-step explanation:
To solve the quadratic equation 2x² + 23x - 6.1 = 0 using the quadratic formula x = (-b ± √(b² - 4ac)) / (2a), we will identify the coefficients: a = 2, b = 23, and c = -6.1.
Substitute these into the formula to find the values of x:
- x = (-23 ± √(23² - 4(2)(-6.1))) / (2(2))
- x = (-23 ± √(529 + 48.8)) / 4
- x = (-23 ± √(577.8)) / 4
- x = (-23 ± 24.037) / 4
Now, we'll calculate the two possible solutions for x:
- x = (-23 + 24.037) / 4 = 0.25925
- x = (-23 - 24.037) / 4 = -11.75925
Therefore, the solutions to the equation are x ≈ 0.25925 and x ≈ -11.75925.