Question

Solve x2 – 6x = 27 by completing the square

Answer 1

\[x^2-6x=27\]
\[(x-3)^2=27+3^2=27+9=36\]
\[x-3=\pm\sqrt{36}=\pm6\]
\[x-3=6\iff x=9\]
\[x-3=-6\iff x=-3\]

Answer 2

x^2-6x=27
x^2-6x-27=0
x^2-2*3x-27=
adding and subtracting 9
x^2-2*3x+9-9-27=0
x^2-2*3x+3^2-36=0
(x-3)^2-6^2=0
a^2-b^2=(a-b)(a+b)
(x-3+6)(x-3-6)=0
(x+3)(x-9)=0
x=-3 ,9