Answer:
x = - 2 ± [tex]\sqrt{5}[/tex]
Step-by-step explanation:
Given
x² + 4x - 1 = 0 ( add 1 to both sides )
x² + 4x = 1
To complete the square
add (half the coefficient of the x- term )² to both sides
x² + 2(2)x + 2² = 1 + 2² ← complete the square on the left side
(x + 2)² = 5 ← take the square root of both sides
x + 2 = ± [tex]\sqrt{5}[/tex] ← subtract 2 from both sides
x = - 2 ± [tex]\sqrt{5}[/tex]
roots are x = - 2 - [tex]\sqrt{5}[/tex] or x = - 2 + [tex]\sqrt{5}[/tex]
