Question

Which is a solution of x2 – x – StartFraction 3 Over 4 EndFraction = 0?

Answer 1

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

Explanation:

Given

x² - x -
`(3)/(4)` = 0 ( add
`(3)/(4)` to both sides )

x² - x =
`(3)/(4)`

Solve using the method of completing the square

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

x² + 2( -
`(1)/(2)` )x +
`(1)/(4)` =
`(3)/(4)` +
`(1)/(4)`

(x -
`(1)/(2)` )² = 1 ( take the square root of both sides )

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

x =
`(1)/(2)` ± 1

Thus

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

x =
`(1)/(2)` + 1 =
`(3)/(2)`