Question

Solve the following equation by transforming it into a perfect square trinomial.



x² – 14x = 15



{–22, 36}


{57, 71}

{–1, 15}


{–15, 29}

Answer 1

x^2 - 14 x  = 15

(x - 7)^2 - 49 = 15

(x-7)^2 = 64

x - 7 = - or  + 8

x = 15  or -1 

Just take half o the coefficient of x and subtract it squared as above.

In general

x^2 + ax = b

(x + a/2)^2 - a^2/4 = b