Question 667139
{{{ (x^2)/2 + x/20 = 10 }}}
You are not simply changing the appearance
of the fractions on the left side. This would be
the case if you did:
{{{ (10/10)*((x^2)/2) + x/20 = 10 }}}
Note that you haven't really changed the value
of the left side
{{{ ( 10x^2 )/ 20 + x/20 = 200/20 }}}
Now you can multiply through by {{{ 20 }}}
{{{ 10x^2 + x = 200 }}}
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What you wanted to do was multiply both sides by {{{ 20 }}}
{{{ (x^2)/2 + x/20 = 10 }}}
{{{ 10x^2 + x = 200 }}}
same answer
{{{ 10x^2 + x - 200 = 0 }}}
You can use the quadratic formula
{{{ x = (-b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 10 }}}
{{{ b = 1 }}}
{{{ c = -200 }}}
{{{ x = (-1 +- sqrt( 1^2 - 4*10*(-200) )) / (2*10) }}}
{{{ x = (-1 +- sqrt( 1 + 8000 )) / 20 }}} 
{{{ x = (-1 +- sqrt( 8001 )) / 20 }}}
{{{ x = ( -1 + 89.4483 ) / 20 }}}
{{{ x = 88.4483 / 20 }}}
{{{ x = 4.4224 }}}
and
{{{ x = ( -1 - 89.4483 ) / 20 }}}
{{{ x = ( -90.4483 ) / 20 }}}
{{{ x = -4.5224 }}}
check:
{{{ ( x - 4.4224 )*( x + 4.5224 ) }}}
{{{ x^2 + .1x - 20 }}}
Multiply both sides by {{{ 1/2 }}}
{{{ (x^2)/2 + x/20 - 10 = 0 }}}
{{{ (x^2)/2 + x/20 = 10 }}}
OK
Why does the book disagree? I don't know