Question

x.(7x-36)=-7

Answer 1

\(x\left(7x-36\right)=-7\\ \Leftrightarrow7x^2-36x+7=0\\ \Leftrightarrow x^2-\dfrac{36}{7}x+1=0\\ \Leftrightarrow x^2-2\cdot x\cdot\dfrac{18}{7}+\dfrac{324}{49}-\dfrac{275}{49}=0\\ \Leftrightarrow\left(x-\dfrac{18}{7}\right)^2-\left(\dfrac{5\sqrt{11}}{7}\right)^2=0\\ \Leftrightarrow\left(x-\dfrac{18}{7}-\dfrac{5\sqrt{11}}{7}\right)\left(x-\dfrac{18}{7}+\dfrac{5\sqrt{11}}{7}\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=\dfrac{18+5\sqrt{11}}{7}\\x=\dfrac{18-5\sqrt{11}}{7}\end{matrix}\right.\)

Vậy \(x=\dfrac{18\pm5\sqrt{11}}{7}\) là nghiệm của phương trình.