Question

$x^2=18x-77$

Answer 1

$$\begin{gathered} \mathrm{Given}: \\ {x}^2=18x-77 \\ \Rightarrow x^2-18x+77=0 \\ \Rightarrow x^2-(11x+7x)+77=0 \\ \Rightarrow x^2-11x-7x+77=0 \\ \Rightarrow x(x-11)-7(x-11)=0 \\ \Rightarrow (x-7)(x-11)=0 \\ \Rightarrow x-7=0\text{or}x-11=0 \\ \Rightarrow x=7\text{or}x=11 \\ \text{Hence, 7 and 11 are the roots of the equation}{x}^2=18x-77. \end{gathered}$$