Solve the inequality4x2 + 4x + 1 < 0

The given inequality is a quadratic inequality which is in the form of ax^2 + bx + c < 0.

Step 1: First, we need to find the roots of the quadratic equation 4x^2 + 4x + 1 = 0.

Step 2: We can use the quadratic formula to find the roots. The quadratic formula is x = [-b ± sqrt(b^2 - 4ac)] / 2a.

Step 3: Substituting the values a = 4, b = 4, and c = 1 into the formula, we get:

x = [-4 ± sqrt((4)^2 - 441)] / 2*4 x = [-4 ± sqrt(16 - 16)] / 8 x = [-4 ± sqrt(0)] / 8 x = [-4 ± 0] / 8

Step 4: So, the roots of the equation are x = -4/8 = -1/2.

Step 5: Since the coefficient of x^2 is positive, the parabola opens upwards. This means that the value of the quadratic expression is less than 0 between the roots.

Step 6: However, in this case, we have a repeated root (x = -1/2). This means that the quadratic expression is never less than 0.

Therefore, the inequality 4x^2 + 4x + 1 < 0 has no solution.