Answer:
x=-3
Step-by-step explanation:
You need to delete the root by ^2. First you need to leave it alone
[tex]\sqrt{x+7}-x=5\\\sqrt{x+7}=5-x\\(\sqrt{x+7} )^{2}=(5-x)^{2} \\x+7=25+10x+x^2\\x-10x=25+x^2-7\\-9x=18+x^2\\-x^2-9x-18=0\\-1(x^2+9x+18)=0\\x^2+9x+18=\frac{0}{-1}\\x^2+9x+18=0\\(x+6)(x+3)=0\\x+6=0 ===> x=-6\\x+3=0 ===> x=-3\\Checking\\\sqrt{-6+7}-(-6)=5===>\sqrt{1}+6=7\neq5 \\\\\sqrt{-3+7}-(-3)=5===>\sqrt{4}+3=5=5\\\\So \\x=-3[/tex]
