Question

How do you solve `sqrt(a-2)+4=a` and check your solution?

Answer 1

`a=6`

Explanation:

We start with:

`sqrt(a-2)+4=a`

Let's bring the 4 over to the right side so that we can square the square root:

`sqrt(a-2)=a-4`

`(sqrt(a-2))^2=(a-4)^2`

`a-2=a^2-8a+16`

Now let's bring all the terms to one side and set it to 0:

`a^2-9a+18=0`

`(a-6)(a-3)=0`

therefore

`a=6, a=3`

And now let's check our solutions:

`sqrt(6-2)+4=6`

`sqrt(4)+4=6`

`2+4=6`

`6=6` `color(green)(Check!)`

~~~~~

`sqrt(3-2)+4=3`

`sqrt(1)+4=3`

`1+4=3`

`5!=3` `color(red)(No!)`

And so our final solution is `a=6`

We can also check this solution by graphing the left side and the right side:

graph{(y-sqrt(x-2)-4)(y-x)=0 [-4.79, 15.21, -1, 9]}