Question

Show all work to solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

Squareroot of x -2 + 8=x

Answer 1

The solution is
`x=11`

Explanation:

we have

`√(x - 2) + 8 = x`

Solve for x

Subtract 8 both sides

`√(x - 2) + 8-8 = x-8`

`√(x - 2)= x-8`

Squared both sides

`(√(x - 2))^2= (x-8)^2`

`(x - 2)= (x-8)^2`

Expand the right side

`(x - 2)= (x^2-16x+64)`

`x^2-17x+66=0`

Solve the quadratic equation by graphing

The solutions are x=6, x=11

see the attached figure

Verify the solutions

For x=6

substitute the value of x in the original equation

`√(6 - 2) + 8 = 6`

`√(4) + 8 = 6`

`2 + 8 = 6`

`10\\eq 6`

therefore

x=6 -----> is an extraneous solution

For x=11

substitute the value of x in the original equation

`√(11 - 2) + 8 = 11`

`√(9) + 8 = 11`

`3 + 8 = 11`

`11=11` ---> is true

therefore

The solution is

`x=11`