Question 125682
Let {{{n}}} = the number
{{{n + 3*sqrt(n) = 28}}}
{{{3*sqrt(n) = 28 - n}}}
square both sides
{{{9n = 784 - 56n + n^2}}}
{{{n^2 - 65n + 784 = 0}}}
use quadratic formula
{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{n = (-(-65) +- sqrt( (-65)^2-4*1*784 ))/(2*1) }}}
{{{n = (65 +- sqrt(4225 - 3136 )) / 2 }}}
{{{n = (65 +- sqrt( 1089 )) / 2 }}}
{{{n = (65 + 33) / 2}}}
{{{n = 49}}}
{{{n = (65 - 33) / 2}}}
{{{n = 16}}} answer
check answer
{{{n + 3*sqrt(n) = 28}}}
{{{16 + 3*sqrt(16) = 28}}}
{{{16 + 3*4 = 28}}}
{{{28 = 28}}}
{{{n = 49}}} only works if you SUBTRACT 3 times the square root from number
{{{n + 3*sqrt(n) = 28}}}
{{{49 - 3*sqrt(49) = 28}}}
{{{49 - 21 = 28}}}
{{{28 = 28}}}