Question

Solve for x:
x^2 -x -1= 0

Answer 1

Possible intermediate steps:
x^2-x-1 = 0
Add 1 to both sides:
x^2-x = 1
Add 1/4 to both sides:
x^2-x+1/4 = 5/4
Factor the left hand side:
(x-1/2)^2 = 5/4
Take the square root of both sides:
sqrt(x-1/2) = sqrt(5)/2
Eliminate the absolute value:
x-1/2 = -sqrt(5)/2 or x-1/2 = sqrt(5)/2
Add 1/2 to both sides:
x = 1/2 (1-sqrt(5)) or x-1/2 = sqrt(5)/2
Add 1/2 to both sides:
x = 1/2 (1-sqrt(5)) or x = 1/2 (1+sqrt(5))