Question

Solve the equation

2x2+8x -1 = 0
by completing the square.
Give your answers correct to 2 decimal places.

Answer 1

x ≈ - 4.12 , x ≈ 0.12

Explanation:

2x² + 8x - 1 = 0 ( add 1 to both sides )

2x² + 8x = 1 ( factor out 2 from the first two terms )

2(x² + 4x) = 1

To complete the square

add/ subtract ( half the coefficient of the x- term )² to x² + 4x

2(x² + 2(2)x + 4 - 4) = 1

2(x + 2)² - 8 = 1 ( add 8 to both sides )

2(x + 2)² = 9 ( divide both sides by 2 )

(x + 2)² =
`(9)/(2)` ( take square root of both sides )

x + 2 = ±
`\sqrt{(9)/(2) }` = ±
`(3)/(√(2) )` ( subtract 2 from both sides )

x = - 2 ±
`(3)/(√(2) )`

Then

x = - 2 -
`(3)/(√(2) )` ≈ - 4.12 ( to 2 dec. places )

x = - 2 +
`(3)/(√(2) )` ≈ 0.12 ( to 2 dec. places )