Question 946105


 {{{(5/8+1/8)+3/8=5/8+(1/8+n)n=0}}}


{{{6/8+3/8=5/8+(1/8+8n/8)n}}} 


{{{9/8=5/8+((1+8n)/8)n}}} 


{{{9/8-5/8=((1+8n)/8)n}}}   


{{{4/8=((1+8n)n)/8}}} 


{{{4/8=n/8+8n^2/8}}} 


{{{4/8=n/8+n^2}}} 


{{{0=n^2+n/8-4/8}}} 


{{{n^2+n/8-4/8=0}}} ...use quadratic formula


{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{n = (-(1/8) +- sqrt( (1/8)^2-4*1*(-4/8) ))/(2*1) }}}

{{{n = (-(1/8)+- sqrt( (1/64)+2))/2 }}}

{{{n = (-(1/8)+- sqrt( (1/64)+128/64))/2 }}}


{{{n = (-(1/8)+- sqrt( 129/64)))/2 }}}


{{{n = (-(1/8)+-sqrt(129)/8)/2 }}}


{{{n = (-1/16 +- sqrt( 129)/16 )}}}


{{{n = (1/16) (-1+- sqrt( 129) )}}}

solutions:

 {{{n = (-1/16 + sqrt( 129)/16 )}}}  -> {{{n = (1/16) (-1+sqrt( 129) )}}}

or

{{{n = (-1/16 - sqrt( 129)/16 )}}}->    {{{n = (1/16) (-1- sqrt( 129) )}}}
                                        


check:


{{{(5/8+1/8)+3/8=5/8+(1/8+(-1/16 + sqrt( 129)/16 ))(-1/16 + sqrt( 129)/16 )}}}


{{{9/8=5/8+(1/8-1/16 -sqrt( 129)/16 )(-1/16 + sqrt( 129)/16 )}}}


{{{9/8=5/8+(2/16-1/16 -sqrt( 129)/16 )(-1/16 + sqrt( 129)/16 )}}}


{{{9/8=5/8-(-(1/16 -sqrt( 129)/16 )(1/16 - sqrt( 129)/16 ))}}}


{{{9/8=5/8-(-(1/16 -sqrt( 129)/16 )^2)}}}


{{{9/8=5/8-(-(0.0625 -0.7098635432250342)^2)}}}


{{{9/8=5/8-(-(-0.6473635432250342)^2)}}}


{{{1.125=0.625-(-(0.4190795570968707))}}}


{{{1.125=0.625+0.4190795570968707}}}


{{{1.125=1.0441}}} round it to whole number


{{{1=1}}}