Question

solve the equation below by completing the square root and solving for x. x^2-6x+1=17

Answer 1

$x^2-6x+1=17\ \ \ |-1\\\\x^2-2\cdot x\cdot3=16\ \ \ |+3^2\\\\\underbrace{x^2-2\cdot x\cdot3+3^2}_{(a-b)^2=a^2-2ab+b^2}=16+3^2\\\\(x-3)^2=25\to x-3=\pm\sqrt{25}\\\\x-3=-5\ \vee\ x-3=5\ \ \ \ |+3\\\\x=-2\ \vee\ x=8$