Solve the equation 4x^2-4x-1=0
1 answer:
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}
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