need help completing the square?

Question

x^2 - x - 1 = 0

i need help to solve with the steps on completing the square without using the quadradic equation. thank you :)

Answer 1

took me an internet site to remember doing this, but it's fairly easy once you get the hang of it...i'll show you how to get the answer in steps:

1) Move the -1 over by adding 1 to each side, so: x^2 - x = 1

2) Take half of the coefficient (the number multiplying the variable) for the x (in this case, -x, so we end up with -1/2) and square it (so now it's 1/4) add it to both sides of the equal sign: x^2 - x + (1/4) = 1 + (1/4)

3) Convert the left side to squared form:
(x-1/4)^2 = 5/4

4) Square root both sides: x - 1/4 = + or - squareroot (5/4)

5) Solve for x : x = 1/4 + or - squareroot of (5/4)
or x = 1/4 + or - (squareroot of 5)/2

Answer 2

x² - x - 1 = 0

Add ¼ to both sides to complete the square

x² - x + ¼ - 1 = ¼

add 1 to both sides to remove -1 from the left

x² - x + ¼ = 1 + ¼

(x - ½)² = 5/4

take the square root of both sides

(x - ½) = ±½ √5

add ½ to both sides

x = ½ ±½ √5 or (1 ±√5)/2
.