Question

Which quadratic equation is equivalent to (x - 4)2 – ( - 4) - 6 = 0?

(u - 4)2 – (u - 4) - 6 = 0 where u = (x - 4)
O v2-(u - 4) - 6 = 0 where u = (x - 4)
O 02 - 16 - 4-6 = 0 where u = (x - 4)
O 02-4-6 = 0 where u = (x - 4)

Answer 1

Answer:D

Explanation:

Answer 2

`u^2-u-6=0`

where

`u=(x-4)`

Explanation:

we have

`(x-4)^2-(x-4)-6=0`

Let

`u=(x-4)`

substitute in the expression above

`(u)^2-(u)-6=0`

Solve for u

Complete the square

`(u^2-u+0.25)=6+0.25`

`(u^2-u+0.25)=6.25`

Rewrite as perfect squares

`(u-0.5)^2=6.25`

square root booth sides

`u-0.5=\pm2.5`

`u=0.5\pm2.5`

`u_1=0.5+2.5=3`

`u_2=0.5-2.5=-2`

Solve for x

Remember that

`u=(x-4)`

For u=3

`3=(x-4)` ---->
`x=7`

For u=-2

`-2=(x-4)` ---->
`x=2`