Question

Solve the equation x² + 6x + 1 = 0. give your answer to two decimal places

Answer 1

x ≈ - 5.83 , x ≈ - 0.17

Explanation:

x² + 6x + 1 = 0 ( subtract 1 from both sides )

x² + 6x = - 1

Using the method of completing the square

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

x² + 2(3)x + 9 = - 1 + 9

(x + 3)² = 8 ( take square root of both sides )

x + 3 = ±
`√(8)` ( subtract 3 from both sides )

x = - 3 ±
`√(8)`

Then

x = - 3 -
`√(8)` ≈ - 5.83 ( to 2 dec. places )

x = - 3 +
`√(8)` ≈ - 0.17 ( to 2 dec. places )