To solve the quadratic expression 4x² + 9x + 4, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / 2a
In this expression, the coefficients are:
- a = 4
- b = 9
- c = 4
Now, let’s calculate the discriminant (b² – 4ac):
b² = 9² = 81
4ac = 4 * 4 * 4 = 64
Now, substitute these values into the discriminant:
b² – 4ac = 81 – 64 = 17
Since the discriminant is positive, we will have two distinct real solutions. Now, we can apply the quadratic formula:
x = (-9 ± √17) / (2 * 4)
Calculating the denominator:
2 * 4 = 8
Now we can calculate the two solutions:
x₁ = (-9 + √17) / 8
x₂ = (-9 – √17) / 8
In summary, the solutions to the equation 4x² + 9x + 4 = 0 are:
x₁ = (-9 + √17) / 8 and x₂ = (-9 – √17) / 8.