Question

Use the quadratic formula to solve 9x^2 + 6x - 17 = 0.

a) x = -1, -5
b) x = 1, 17/9
c) x = -3, 17/3
d) x = 2, -17/3

Answer 1

To solve the equation 9x^2 + 6x - 17 = 0 using the quadratic formula, substitute the values of a, b, and c into the formula. Simplify the equation and solve for x, resulting in x = (-1 ± √(2))/(3).

Step-by-step explanation:

To solve the equation 9x^2 + 6x - 17 = 0 using the quadratic formula, we need to identify the values of a, b, and c. In this case, a = 9, b = 6, and c = -17. Substituting these values into the quadratic formula, we get:

x = (-6 ± √(6^2 - 4 * 9 * -17))/(2 * 9)

Simplifying further, we have:

x = (-6 ± √(36 + 612))/(18)

x = (-6 ± √(648))/(18)

x = (-6 ± √(36 * 18))/(18)

x = (-6 ± 6√(2))/(18)

x = (-1 ± √(2))/(3)

Therefore, the solutions to the equation 9x^2 + 6x - 17 = 0 are x = (-1 ± √(2))/(3).