Question 559338
{{{  x^2+12x = 15  }}}
You can solve by completing the square.
Take 1/2 of the coefficient of {{{x}}},
square it, and add it to both sides
{{{ x^2 + 12x + (12/2)^2 = 15 + (12/2)^2 }}}
{{{ x^2 + 12x + 36 = 15 + 36 }}}
{{{ ( x + 6 )^2 = 51 }}}
Take the square root of both sides
{{{ x + 6 = sqrt( 51 ) }}}
{{{ x = sqrt(51) - 6 }}}
and also, taking the negative square root,
{{{ x = -sqrt(51) - 6 }}}
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I will attempt to check the 1st solution
{{{ ( sqrt(51) - 6)^2+12*( sqrt(51) - 6) = 15 }}}
{{{ 51 - 12*sqrt(51) + 36 + 12*sqrt(51) - 72 = 15 }}}
{{{ 51 + 36 - 72 = 15 }}}
{{{ 15 = 15 }}}
OK
You can check the other solution, {{{ x = -sqrt(51) - 6 }}}