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

Answer:

The solution is $x=11$

Step-by-step explanation:

we have

$\sqrt{x - 2} + 8 = x$

Solve for x

Subtract 8 both sides

$\sqrt{x - 2} + 8-8 = x-8$

$\sqrt{x - 2}= x-8$

Squared both sides

$(\sqrt{x - 2})^2= (x-8)^2$

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

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

$\sqrt{6 - 2} + 8 = 6$

$\sqrt{4} + 8 = 6$

$2 + 8 = 6$

$10\neq 6$  

therefore

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

For x=11

substitute the value of x in the original equation

$\sqrt{11 - 2} + 8 = 11$

$\sqrt{9} + 8 = 11$

$3 + 8 = 11$

$11=11$  ---> is true

therefore

The solution is

$x=11$