Question

Solve the equation for all values of x by completing the square. x^2+8x=9

Answer 1

$(*)\qquad(a+b)^2=a^2+2ab+b^2\\\\x^2+8x=9\\\\x^2+2\cdot x\cdot4=9\ \ \ \ |+4^2\\\\\underbrace{x^2+2\cdot x\cdot4+4^2}_{(*)}=9+4^2\\\\(x+4)^2=25\to x+4=\pm\sqrt{25}\\\\x+4=-5\ \vee\ x+4=5\ \ \ \ \ |-4\\\\x=-9\ \vee\ x=1$