Question

Solve for all possible values of x. square root of the quantity x plus 6 end quantity plus 5 equals 17

Answer 1

Answer:

$x=138$

Step-by-step explanation:

So we have the equation:

$\sqrt{x+6}+5=17$

First, let's determine the domain restrictions. Recall that the radicand cannot be negative. In other words, it must be greater than or positive than 0. Thus:

$x+6\geq 0$

Subtract 6 from both sides:

$x\geq -6$

What this means is that our solutions must be greater than or equal to -6. If not, we ignore them.

So, let's subtract 5 from both sides from the original equation:

$\sqrt{x+6}=12$

Square both sides:

$x+6=144$

Subtract 6 from both sides:

$x=138$

138 is greater than -6, so 138 is a solution and is the only solution.

And we're done!