Question 1079108
Let {{{ x }}} = Peter's current age
given:
{{{ x + 11 = (1/2)*( x - 13 )^2 }}}
{{{ 2*( x + 11 ) = x^2 - 26x + 169 }}}
{{{ 2x + 22 = x^2 - 26x + 169 }}}
{{{ x^2 -28x + 147 = 0 }}}
Use quadratic equation
{{{ x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = -28 }}}
{{{ c = 147 }}}
----------------
{{{ x = ( -(-28) +- sqrt( (-28)^2-4*1*147 ))/(2*1) }}} 
{{{ x = ( 28 +- sqrt( 784 - 588 ))/2 }}} 
{{{ x = ( 28 +- sqrt( 196 ))/2 }}} 
{{{ x = ( 28 + 14 ) / 2 }}}
{{{ x = 42/2 }}}
{{{ x = 21 }}}
Peter is 21 now
------------------
check:
{{{ x + 11 = (1/2)*( x - 13 )^2 }}}
{{{ 21 + 11 = (1/2)*( 21 - 13 )^2 }}}
{{{ 32 = (1/2)*8^2 }}}
{{{ 32 = (1/2)*64 }}}
{{{ 32 = 32 }}}
OK
I'll try the negative root of {{{ 196 }}} also
{{{ x = ( 28 - 14 ) / 2 }}}
{{{ x = 14/2 }}}
{{{ x = 7 }}}
-----------------
{{{ x + 11 = (1/2)*( x - 13 )^2 }}}
{{{ 7 + 11 = (1/2)*( 7 - 13 )^2 }}}
{{{ 18 = (1/2)*( -6 )^2 }}}
{{{ 18 = (1/2)*36 }}}
{{{ 18 = 18 }}}
I don't think this is a valid solution since his
age 13 years ago ends up being 6 years 
before he was born. I'll stick with
the 1st answer.