Question 34171
{{{ x^2 + 8x-3 = 0 }}}
To complete the square, you must make the left side a perfect square trinomial.
Add three to both sides
{{{ x^2 + 8x = 3 }}}
using {{{ (b/2)^2 }}} find the number that will "complete the square"
{{{ (8/2)^2 = 4^2 = 16 }}}
Add 16 to both sides
{{{ x^2 + 8x + 16 = 3 + 16 }}} 
Factor the left ... add the right
{{{ (x+4)^2 = 19 }}}
Squareroot both sides
{{{ x+4 = sqrt(19) }}}
subtract 4 from both sides
{{{ x = -4 +- sqrt(19) }}}
Remember that there is a + and a - since there has to be two solutions for a perfect square trinomial