Question

Find the solution to the following equation by transforming it into a perfect square trinomial.

Answer 1

$x^{2} -12x=13\ \ \ \Leftrightarrow\ \ \ x^2-2\cdot x\cdot 6+6^2-6^2=13\\\\ \Leftrightarrow\ \ \ (x-6)^2=13+36\ \ \ \Leftrightarrow\ \ \ (x-6)^2=49\ \ \ \Leftrightarrow\ \ \ (x-6)^2=7^2\\\\x-6=7\ \ \ \ \ \ \ or\ \ \ \ \ \ \ \ x-6=-7\\\\x=13\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x=-1\\\\Ans.\ x\in \{-1,\ 13\}$

Answer 2

X² -12x  = 13                       way to obtain 36   >       (-12/2)²  =  36    
x²  -12x + 36 =13 +36      since we add 36 to the left,we must also add 36 to the right
(x-6)²  =  49
x-6  =    7
x  =    7 + 6 =  13    or      -7 + 6  = -1
x =  -1    or    13