Answer:
[tex]x=7[/tex]
Step-by-step explanation:
[tex]x =\sqrt{(x+18)}+2[/tex]
subtract 2 from both sides:
[tex]x -2=\sqrt{(x+18)}[/tex]
square both sides:
[tex](x -2)^2=x+18[/tex]
expand brackets:
[tex]x^2-4x+4=x+18[/tex]
subtract x from both sides:
[tex]x^2-5x+4=18[/tex]
subtract 18 from both sides:
[tex]x^2-5x-14=0[/tex]
factor:
[tex]x^2+2x-7x-14=0[/tex]
[tex]x(x+2)-7(x+2)=0[/tex]
[tex](x+2)(x-7)=0[/tex]
solve for x:
[tex]x+2=0\implies x=-2[/tex]
[tex]x-7=0\implies x=7[/tex]
Now we have found the values of x, input them into the original equation to verify:
when [tex]x = -2[/tex]:
[tex]\sqrt{(-2 +18)}+2=6\\\\ 6\neq 2\implies \textsf {incorrect}[/tex]
when [tex]x = 7[/tex]:
[tex]\sqrt{(7+18)}+2=7\\\\ 7=7\implies \textsf {correct}[/tex]
Therefore, the only correct solution is [tex]x=7[/tex]
Let's find x
[tex]\\ \rm\rightarrowtail x=\sqrt{x+18}+2[/tex]
[tex]\\ \rm\rightarrowtail x-2=\sqrt{x+18}[/tex]
[tex]\\ \rm\rightarrowtail x^2-4x+4={x+18}[/tex]
[tex]\\ \rm\rightarrowtail x^2-5x-14=0[/tex]
[tex]\\ \rm\rightarrowtail x^2+2x-7x-14=0[/tex]
[tex]\\ \rm\rightarrowtail (x+2)(x-7)=0[/tex]
