Solve the following equation by transforming it into a perfect square trinomial.
x2 – 4x = 5

A.
{–5, 13}

B.
{–7, 11}

C.
{1, 7}

D.
{–1, 5}

Question

Solve the following equation by transforming it into a perfect square trinomial.
x2 – 4x = 5
 
 A.
{–5, 13}
 
 B.
{–7, 11}
 
 C.
{1, 7}
 
 D.
{–1, 5}

anonymous · Answer

so when creating a perfect square trinomial, we add a number to both sides so we can factor the equation easier and we find this number we add using (b/2)^2
b=-4 in this case so (-4/2)^2=(-2)^2=4 so now we add 4 to both sides
x^2–4x+4=5+4 this makes x^2-4x+4 into a perfect square of (x-2)^2 so
(x-2)^2=9          now to solve for x we square root the equation to get rid of the exponent
x-2=+-3            and now we set x-2 equal to both +3 and -3 since both squared =9
x-2=-3              x-2=+3        for both you add 2 to both sides
x=-1                  x=5              so the answer is D