Question

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

Square root of the quantity x-6 end quantity - 4 =x

Answer 1

x=-2 is the only solution

Explanation:

The given equation is

`√(x+6)-4=x`

Add 4 to both sides of the equation.

`√(x+6)=x+4`

Square both sides

`x+6=(x+4)^2`

`x+6=x^2+8x+16`

Rewrite in standard form;

`x^2+8x-x+16-6=0`

`x^2+7x+10=0`

`x^2+7x+10=0`

`(x+2)(x+5)=0`

x=-2 or x=-5

Checking for extraneous solution.

When x=-2

`√(-2+6)-4=-2`

`√(4)-4=-2`

`2-4=-2`. This statement is true. This implies that: x=-2 is a solution.

When x=-5

`√(-5+6)-4=-5`

`√(1)-4=-5`

`1-4=-5`. This statement is not true. This implies that: x=-5 is an extranous solution.