Question

Find the roots of the quadratic function by completing the square: x^2 + 4x - 1 = 0

Answer 1

x = - 2 ±
`√(5)`

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 = ±
`√(5)` ← subtract 2 from both sides

x = - 2 ±
`√(5)`

roots are x = - 2 -
`√(5)` or x = - 2 +
`√(5)`