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

${x}_{1} = 1 + \sqrt{6}$

${x}_{2} = 1 - \sqrt{6}$

Explanation:

We start from the given equation

$x \left(x - 2\right) = 5$

Expand it to make it a trinomial

${x}^{2} - 2 x = 5$

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.

${x}^{2} - 2 x + 1 = 5 + 1$

${\left(x - 1\right)}^{2} = 6$

Take the square root of both sides of the equation

$\sqrt{{\left(x - 1\right)}^{2}} = \pm \sqrt{6}$

$x - 1 = \pm \sqrt{6}$

$x = + 1 \pm \sqrt{6}$

${x}_{1} = 1 + \sqrt{6}$

${x}_{2} = 1 - \sqrt{6}$

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