Answer:
[tex]x=138[/tex]
Step-by-step explanation:
So we have the equation:
[tex]\sqrt{x+6}+5=17[/tex]
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:
[tex]x+6\geq 0[/tex]
Subtract 6 from both sides:
[tex]x\geq -6[/tex]
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:
[tex]\sqrt{x+6}=12[/tex]
Square both sides:
[tex]x+6=144[/tex]
Subtract 6 from both sides:
[tex]x=138[/tex]
138 is greater than -6, so 138 is a solution and is the only solution.
And we're done!
