Question 804559
{{{x^2+2x=3}}}
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Steps:
{{{x^2+2x-3=3-3}}}
{{{x^2+2x-3=0}}}
The part of the left side expression, {{{x^2+2x}}}, is like a rectangle of sides x and x+2.  The missing square piece, when part of the rectangle is rearranged visually would be {{{(2/2)^2=1}}}.
THAT is what you add to both sides of the general form equation to Complete the Square.
{{{x^2+2x+1 -3 = 0+1}}}
{{{(x+1)^2-3=1}}}
{{{(x+1)^2=1+3}}}
{{{(x+1)^2=4}}}
{{{x+1=0+- 2}}}----the zero is included here only so the site rendering works.  It is not needed when done on paper.
{{{x=-1+2}}} or {{{x=-1-2}}}
{{{highlight(x=1)}}} or {{{highlight(x=-3)}}}