Question

Solve the equation 4x^2-4x-1=0

Answer 1

Answer:

  x = (1 ±√2)/2

Step-by-step explanation:

We can "complete the square" to solve this.

  4x^2 -4x = 1 . . . . add 1

  x^2 -x = 1/4 . . . . .divide by 4 to make x^2 coefficient = 1

  x^2 -x +1/4 = 2/4 . . . . add the square of half the x-coefficient: (-1/2)^2 = 1/4

  (x -1/2)^2 = 2/4  . . . . write as a square

  x -1/2 = ±(√2)/2 . . . . . take the square root

  x = (1 ±√2)/2 ≈ {-0.2071, 1.2071}