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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}

Verified Answer :

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

kate200468

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

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