Question

If f(x)= x^2-2x and g(x)= 6x+4, for which value of x does (f+g)(x)=0

Answer 1

$f(x)=x^2-2x;\ g(x)=6x+4\\\\(f+g)(x)=(x^2-2x)+(6x+4)=x^2+4x+4$

$(f+g)(x)=0\iff x^2+4x+4=0\\\\x^2+2x+2x+4=0\\\\x(x+2)+2(x+2)=0\\\\(x+2)(x+2)=0\\\\(x+2)^2=0\iff x+2=0\ \ \ |-2\\\\\boxed{x=-2}$