Question

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

Answer 1

`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.