Question

Solve x²-4x-1=0 in the form a+-square root b

Answer 1

x = 2 ±
`√(5)`

Explanation:

Given

x² - 4x - 1 = 0 ( add 1 to both sides )

x² - 4x = 1

Using the method of completing the square

Add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2) x + 4 = 1 + 4

(x - 2)² = 5 ( take the square root of both sides )

x - 2 = ±
`√(5)` ( add 2 to both sides )

x = 2 ±
`√(5)`