Question 601411
To complete the square, take 1/2 of the
coefficient of the {{{ x }}} term, square it,
and add it to both sides.
{{{ x^2 + 8x = 14 }}}
{{{ x^2 + 8x + (8/2)^2 = 14 + (8/2)^2 }}}
{{{ x^2 + 8x + 16 = 14 + 16 }}}
{{{ ( x + 4 )^2 = 30 }}}
Take the square root of both sides
{{{ x + 4 = sqrt(30) }}}
{{{ x = -4 + sqrt(30) }}}
and also, taking the negative square root,
{{{ x = -4 - sqrt(30) }}}
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check the answers:
{{{ ( -4 - sqrt(30) )^2 + 8*(  -4 -  sqrt(30)) = 14 }}}
{{{ 16 + 8*sqrt(30) + 30 - 32 - 8*sqrt(30) = 14 }}}
{{{ 16 + 30 - 32 = 14 }}}
{{{ 14 = 14 }}}
OK- you can check the other answer