Question 454574
{{{ x^2 + 6x + 8 = 0 }}}
First subtract {{{ 8 }}} from both sides
{{{ x^2 + 6x = -8 }}}
Take 1/2 of the coefficient of {{{x}}},
square it, and add it to both sides
{{{ x^2 + 6x + (6/2)^2 = -8 + (6/2)^2 }}}
{{{ x^2 + 6x + 9 = -8 + 9 }}}
{{{ x^2 + 6x + 9 = 1 }}}
Note that both sides are now perfect squares
and can be written as:
{{{ ( x + 3 )^2 = 1^2 }}}
Take the square root of both sides
{{{ x + 3 = 1 }}}
{{{ x = -2 }}} 1st answer
Note that there is also a negative square root of {{{ 1^2 }}}
{{{ x + 3 = -1 }}}
{{{ x = -4 }}} 2nd answer
Now I can check answers by rewriting the answers as:
{{{ x + 2 = 0 }}}
{{{ x + 4 = 0 }}}
These are the factor of the equation, so:
{{{ (x + 2)*( x + 4 ) = 0 }}}
{{{ x^2 + 6x + 8 = 0 }}}
OK