Question

Solve the following quadratic equation using the perfect square trinomial pattern: 14x2+2x+4=0.

Answer 1

Solve 14x^2 + 2x + 4 = 0 by completing the square.

1. Divide by 14:
x^2 + (1/7)x + 2/7 = 0

2. Move constant to the right:
x^2 + (1/7)x = -2/7

3. Complete the square: half of 1/7 is 1/14, square is 1/196. Add to both sides:
x^2 + (1/7)x + 1/196 = -2/7 + 1/196
(x + 1/14)^2 = -55/196

4. Take square roots:
x + 1/14 = ± i·√55 / 14

5. Solve for x:
x = -1/14 ± (i√55)/14 = (-1 ± i√55)/14

So the solutions are x = (-1 ± i√55)/14.