9x²+24x+16=0

To solve the quadratic equation \(9x^2 + 24x + 16 = 0\), we can use the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this equation, \(a = 9\), \(b = 24\), and \(c = 16\). 1. **Calculate the discriminant (\(D\)):** \[ D = b^2 - 4ac = 24^2 - 4 \times 9 \times 16 \] \[ D = 576 - 576 = 0 \] 2. **Since the discriminant is 0, there is one real double root. Now substitute the values into the quadratic formula:** \[ x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-24 \pm 0}{2 \times 9} \] \[ x = \frac{-24}{18} = \frac{-4}{3} \] Therefore, the solution to the equation \(9x^2 + 24x + 16 = 0\) is: \[ x = -\frac{4}{3} \] This is the only solution since the discriminant is zero, indicating a double root.