Question

Solve the equation 2x² + 2x - 5 = 0.
Give your answers correct to 2 decimal places.​

Answer 1

x ≈ - 2.16 , x ≈ 1.16

Explanation:

using the method of completing the square to solve

2x² + 2x - 5 = 0 ( add 5 to both sides )

2x² + 2x = 5

factor out 2 from each term on the left side

2(x² + x) = 5

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

2(x² + 2(
`(1)/(2)` )x +
`(1)/(4)` -
`(1)/(4)` ) = 5

2(x +
`(1)/(2)` )² -
`(1)/(2)` = 5 ( add
`(1)/(2)` to both sides )

2(x +
`(1)/(2)` )² = 5
`(1)/(2)` =
`(11)/(2)` ( divide both sides by 2 )

(x +
`(1)/(2)` )² =
`(11)/(4)` ( take square root of both sides )

x +
`(1)/(2)` = ±
`\sqrt{(11)/(4) }` = ±
`(√(11) )/(2)` ( subtract
`(1)/(2)` from both sides )

x = -
`(1)/(2)` ±
`(√(11) )/(2)`

Then

x = -
`(1)/(2)` -
`(√(11) )/(2)` ≈ - 2.16 ( to 2 dec. places )

x = -
`(1)/(2)` +
`(√(11) )/(2)` ≈ 1.16 ( to 2 dec. places )