Question 630090
That is correct
{{{ x ^2 + x = 42 }}}
complete the square
Take 1/2 of the coefficient of
{{{ x }}}, square it, and add it
to both sides
{{{ x^2 + x + (1/2)^2 = 42 + (1/2)^2 }}}
{{{ x^2 + x + 1/4 = 42 + 1/4 }}}
{{{ x^2 + x + 1/4 = 168/4 + 1/4 }}}
{{{ x^2 + x + 1/4 = 169/4 }}}
{{{ ( x + 1/2 )^2 = (13/2)^2 }}}
Take the square root of both sides
{{{ x + 1/2 = 13/2 }}}
{{{ x = 12/2 }}}
{{{ x = 6 }}}
The number is 6
check:
{{{ x ^2 + x = 42 }}}
{{{ 6 ^2 + 6 = 42 }}}
{{{ 36 + 6 = 42 }}}
{{{ 42 = 42 }}}
OK