To solve the equation 2x2 + 7x + 9 = 0, I would choose the quadratic formula method. The quadratic formula is given as:
x = (-b ± √(b² – 4ac)) / 2a
In this equation, a is 2, b is 7, and c is 9. The reason I selected this method is that the coefficients do not factor easily into rational numbers, making it complicated to solve by factoring. The quadratic formula allows us to find the solutions for any quadratic equation, regardless of whether it can be factored neatly.
Plugging in the values into the quadratic formula:
- Calculate the discriminant: b² – 4ac = 7² – 4(2)(9) = 49 – 72 = -23
Since the discriminant is negative, this tells us that the equation does not have real solutions; instead, it will have complex solutions. Thus, using the quadratic formula is not only appropriate for finding the solutions but necessary for understanding the nature of the roots of the equation.