To solve the quadratic equation 3x² + 14x + 16 = 0, we can use the quadratic formula, which is:
x = (-b ± √(b² – 4ac)) / 2a
In our case, the coefficients are:
- a = 3
- b = 14
- c = 16
Now, let’s calculate the discriminant, which is the part under the square root:
b² – 4ac = 14² – 4(3)(16) = 196 – 192 = 4
Since the discriminant is positive, we know there will be two distinct real solutions. Now we can apply the quadratic formula:
x = (-14 ± √4) / (2 * 3)
This simplifies to:
x = (-14 ± 2) / 6
Now we can find the two solutions:
- x₁ = (-14 + 2) / 6 = -12 / 6 = -2
- x₂ = (-14 – 2) / 6 = -16 / 6 = -8/3
Thus, the solutions to the equation 3x² + 14x + 16 = 0 are:
- x₁ = -2
- x₂ = -8/3