To find the values of x in the equation 4x² + 4x + 3 = 0, we can use the quadratic formula, which is given by:
x = (-b ± √(b² – 4ac)) / (2a)
In this equation, a = 4, b = 4, and c = 3.
First, we need to determine the value of the discriminant, b² – 4ac:
b² = 4² = 16
4ac = 4 * 4 * 3 = 48
Discriminant = 16 – 48 = -32
Since the discriminant is negative (-32), it means that the quadratic equation does not have real solutions. Instead, it has two complex solutions.
Now, we proceed with calculating the solutions using the quadratic formula:
x = (-4 ± √(-32)) / (2 * 4)
This simplifies to:
x = (-4 ± 4i√2) / 8
Breaking this down further, we get:
x = -1/2 ± (i√2)/2
Thus, the values of x where the equation 4x² + 4x + 3 = 0 holds true are:
- x = -1/2 + (i√2)/2
- x = -1/2 – (i√2)/2