Question

Find the roots of the quadratic equation x^2 -8x=9 by completing the square

Answer 1

`Use:(a-b)^2=a^2-2ab+b^2\ \ \ (*)\\--------------------\\\\x^2-8x=9\\\\x^2-2x\cdot4=9\ \ \ |add\ 4^2\ to\ both\ sides\\\\\underbrace{x^2-2x\cdot4+4^2}_(use\ (*))=9+4^2\\\\(x-4)^2=9+16\\\\(x-4)^2=25\iff x-4=\pm√(25)\\\\x-4=-5\ or\ x-4=5\ \ \ |add\ 4\ to\ both\ sides\\\\\boxed{x=-1\ or\ x=9}`