Question

What value of c will complete the square in the expression below to make it a perfect square trinomial? x² - 9x + c Enter the perfect square trinomial as a squared binomial.​

Answer 1

c =
`(81)/(4)`

Explanation:

x² - 9x + c

to complete the square

add ( half the coefficient of the x- term)² to x² - 9x

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

= x² - 9x +
`(81)/(4)` → with c =
`(81)/(4)`

= (x -
`(9)/(2)` )²