Question 443026
{{{s^2 -2s = 5}}}

Solve for 0.

{{{s^2 - 2s -5 = 0}}}

Factor if possible:

What adds up to -2 and multiples to -5?

Unfortunately 5 is prime, so 1 and 5 are the only factors.

Let's complete the square.

{{{s^2 -2s =5}}}

To complete the square, we must take {{{(b/2)^2}}} and make that the c term.

{{{(-2/2)^2 = 1}}}

{{{s^2 - 2s + 1  = 5 + 1 }}} we must add 1 to keep the equation balanced.

{{{(s-1)^2 = 6}}}
{{{sqrt(s-1)^2 = sqrt(6)}}}
{{{s-1 = 0+- sqrt(6)}}}
{{{s = 1+- sqrt(6)}}}