Question

2x²+5x-3=0
using completing the square method​

Answer 1

`2 {x}^(2) + 5x - 3 = 0 \\ 2( {x}^(2) + (5)/(2) x - (3)/(2) ) = 0 \\ 2( {x}^(2) + (5)/(2) x + {( (5)/(4) )}^(2) ) - (3)/(2) - {( (5)/(4) )}^(2) ) = 0 \\ ( {(x + (5)/(4) )}^(2) = (49)/(16) \\ x + (5)/(4) = ± (7)/(4) \\ x = 0.5 \: \: and \: \: 3`

Answer 2

x=
`(1)/(2)` or x= -3

Explanation:

`\boxed{x^(2) +kx=(x+(k)/(2))^(2) -((k)/(2))^(2) }`

First ensure that the coefficient of x² is 1.

x² +
`(5)/(2)`x -
`(3)/(2)`= 0

[x +(
`(5)/(2)` ÷2)]² -(
`(5)/(2)` ÷2)² -
`(3)/(2)`= 0

(x +
`(5)/(4)`)² -(
`(5)/(4)`)² -
`(3)/(2)`= 0

(x +
`(5)/(4)`)²-
`(25)/(16)` -
`(3)/(2)`= 0

(x +
`(5)/(4)`)² -
`(49)/(16)`= 0

(x +
`(5)/(4)`)²=
`(49)/(16)`

x +
`(5)/(4)`=
`\sqrt{(49)/(16) }` (square root both sides)

x +
`(5)/(4)`= ±
`(7)/(4)`

x= -
`(5)/(4)` +
`(7)/(4)` or x= -
`(5)/(4)` -
`(7)/(4)`

x=
`(1)/(2)` or x= -3