To solve the equation 2x2 + 7x + 9 = 0, I would choose the quadratic formula method. The quadratic formula states that for any quadratic equation of the form ax2 + bx + c = 0, the solutions for x can be found using:
x = (-b ± √(b2 – 4ac)) / 2a
In this case, the coefficients are: a = 2, b = 7, and c = 9. Plugging these values into the formula will help us find the values of x.
Firstly, we need to calculate the discriminant:
b2 – 4ac = 72 – 4 * 2 * 9 = 49 – 72 = -23
Since the discriminant is negative (-23), this indicates that there are no real roots for this equation; instead, the solutions will be complex numbers.
To find the complex solutions, we can continue using the quadratic formula:
x = (-7 ± √(-23)) / (2 * 2)
This simplifies to:
x = (-7 ± i√23) / 4
Thus, the solutions to the equation 2x2 + 7x + 9 = 0 are:
x = (-7 + i√23) / 4 and x = (-7 – i√23) / 4.
In conclusion, I chose the quadratic formula due to its effectiveness in handling any quadratic equation, especially when the coefficients lead to a situation where the discriminant is negative. This method provides a clear pathway to finding both real and complex solutions and is highly systematic in approach.