Question

What is x^2-9x+4=0? please help.. i’m using this method: (x+b)^2-b^2=x^2+2bx

Answer 1

see explanation

Explanation:

Given

x² - 9x + 4 = 0 ( subtract 4 from both sides )

x² - 9x = - 4

Using the method of completing the square

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

x² +2 (-
`(9)/(2)`)x +
`(81)/(4)` = - 4 +
`(81)/(4)`

(x -
`(9)/(2)`)² =
`(65)/(4)`

Take the square root of both sides

x -
`(9)/(2)` = ±
`\sqrt{(65)/(4) }` = ±
`(1)/(2)`
`√(65)`

Add
`(9)/(2)` to both sides

x =
`(9)/(2)` ±
`(1)/(2)`
`√(65)` ← exact solutions