Question

find the solution to the equation by completing the square x^2-6x=7. what is the smallest and largest value of x

Answer 1

smallest value of x = -1

Largest value of x = 7

Explanation:

`x^2-6x=7`

coefficient of x = -6

Half of the coefficient of x = -6/2 = -3

Square of the half value
`=(-3)^2=9`

Add the square value on both sides of equation

`x^2-6x+9=7+9`

`(x-3)^2=16`

Take square root

`x-3= \pm √(16)`

`x-3= \pm 4`

`x-3=+4` or
`x-3=-4`

`x=+4+3` or
`x=-4+3`

`x=7` or
`x=-1`

Hence smallest value of x = -1

Largest value of x = 7