Question 634449
{{{ y^2 - 18y + 81 = 25 }}}
{{{ y^2 - 18y = -56 }}}
Complete the square
{{{ y^2 - 18y + (18/2)^2 = -56 + (18/2)^2 }}}
{{{ y^2 - 18y + 81 = -56 + 81 }}}
This ends up being what I started with,
since I didn't realize both sides were
perfect squares, but now I've proven it
{{{ ( y - 9 )^2  = 5^2 }}}
Take the square root of both sides
{{{ y - 9 = 5 }}}
{{{ y = 14 }}}
and taking negative square root of {{{ 5^2 }}}
{{{ y - 9 = -5 }}}
{{{ y = 4 }}}
I can check by plugging both results back into equation
{{{ y^2 - 18y + 81 = 25 }}}
{{{ 14^2 - 18*14 + 81 = 25 }}}
{{{ 196 - 252 + 81 = 25 }}}
{{{ 25 = 25 }}}
and
{{{ 4^2 - 18*4 + 81 = 25 }}}
{{{ 16 - 72 + 81 = 25 }}}
{{{ 25 = 25 }}}
OK