Question

X²+x-90=0 using completing the square method
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Answer 1

x = - 10, x = 9

Explanation:

Given

x² + x - 90 = 0 ( add 90 to both sides )

x² + x = 90

To complete the square

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

x² + 2(
`(1)/(2)` )x +
`(1)/(4)` = 90 +
`(1)/(4)`

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

x +
`(1)/(2)` = ±
`\sqrt{(361)/(4) }` = ±
`(19)/(2)` ( subtract
`(1)/(2)` from both sides )

x = -
`(1)/(2)` ±
`(19)/(2)` , thus

x = -
`(1)/(2)` -
`(19)/(2)` =
`(-20)/(2)` = - 10

x = -
`(1)/(2)` +
`(19)/(2)` =
`(18)/(2)` = 9