Question

Solve the equation 2x^2+8x-1=o by completing the square. Give your answer to 2 decimal places

Answer 1

x ≈ - 4.12 , x ≈ 0.12

Explanation:

Given

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

2x² + 8x = 1 ← factor out 2 on the left side

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, that is

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 the square root of both sides )

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

x = - 2 ± 1.5
`√(2)` , thus

x = - 2 - 1.5
`√(2)` ≈ - 4.12 ( to 2 dec. places )

x = - 2 + 1.5
`√(2)` ≈ 0.12 ( to 2 dec. places )