How do you solve using the completing the square method # x(x - 2) = 5#?

1 Answer

Answer:

#x_1=1+sqrt6#

#x_2=1-sqrt6#

Explanation:

We start from the given equation

#x(x-2)=5#

Expand it to make it a trinomial

#x^2-2x=5#

We add 1 to both sides of the equation. The number #1# is derived from numerical coefficient of x which is #-2#. Divide -2 by 2 then square the result which is 1.

#x^2-2x+1=5+1#

#(x-1)^2=6#

Take the square root of both sides of the equation

#sqrt((x-1)^2)=+-sqrt6#

#x-1=+-sqrt6#

#x=+1+-sqrt6#

#x_1=1+sqrt6#

#x_2=1-sqrt6#

God bless....I hope the explanation is useful.