Final answer:
To solve 4x²+4x+2=0 using the quadratic formula, substitute the values of a, b, and c into the formula x = (-b ± sqrt(b²-4ac)) / (2a). The resulting complex solutions are x = -0.5 ± 0.5i.
Step-by-step explanation:
To solve the quadratic equation 4x²+4x+2=0 using the quadratic formula, we can plug the values of a=4, b=4, and c=2 into the formula: x = (-b ± sqrt(b²-4ac)) / (2a). Substituting these values, we have x = (-4 ± sqrt(4²-4(4)(2))) / (2(4)). Simplifying further, we get x = (-4 ± sqrt(16-32)) / 8, which simplifies to x = (-4 ± sqrt(-16)) / 8.
Since the discriminant (b²-4ac) is negative, the equation has no real solutions. The solutions are complex numbers. Using the square root of -16, we have x = (-4 ± 4i) / 8. Simplifying this, we get x = -0.5 ± 0.5i.