Question

solve the equation by completing the square: x^2-3x-18=0. after completing the square, the equation will be ______ and the solution is ______

Answer 1

x=3; x=-6

Explanation:

and positve

Answer 2

x = - 3, x = 6

Explanation:

x² - 3x - 18 = 0 ( add 18 to both sides )

x² - 3x = 18

To complete the square

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

x² + 2(-
`(3)/(2)` )x +
`(9)/(4)` = 18 +
`(9)/(4)`

(x -
`(3)/(2)` )² =
`(81)/(4)` ( take square root of both sides )

x -
`(3)/(2)` = ±
`\sqrt{(81)/(4) }` = ±
`(9)/(2)` ( add
`(3)/(2)` to both sides )

x =
`(3)/(2)` ±
`(9)/(2)`

Then

x =
`(3)/(2)` -
`(9)/(2)` =
`(-6)/(2)` = - 3

x =
`(3)/(2)` +
`(12)/(2)` = 6