Answer:
The solution of given equation are x = −6 x = −1.
Step-by-step explanation:
The given equation is
\(\sqrt{x+10}-4=x\)
Add 4 on both sides.
\(\sqrt{x+10}=x+4\)
Square both side.
\(x+10=(x+4)^2\)
\(x+10=x^2+8x+16\)
\(0=x^2+7x+6\)
\(0=x^2+6x+x+6\)
\(0=x(x+6)+1(x+6)\)
\(0=(x+6)(x+1)\)
Use zero product property and equate each factor equal to 0.
\(x+6=0\Rightarrow x=-6\)
\(x+1=0\Rightarrow x=-1\)
Therefore the solution of given equation are x = −6 x = −1.
