Question

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

x2 – 12x = 13

       {46, 55}
       {–1, 13}
       {–15, 27}
       {–21, 33}

Answer 1

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

Answer 2

`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\}`