Question

Solve this radical equation (square root of x+11)-x=-1

Answer 1

`\bf √(x+11)-x=-1\implies √(x+11)=x-1\implies \stackrel{\textit{squaring both sides}}{(√(x+11))^2=(x-1)^2} \\\\\\ x+11=\stackrel{\mathbb{F~O~I~L}}{x^2-2x+1}\implies 11=x^2-3x+1\implies 0=x^2-3x-10 \\\\\\ 0=(x-5)(x+2)\implies x= \begin{cases} 5\\ -2 \end{cases}`