Question

x(squared)+2x-3=0 solve by completing the square???

Answer 1

Move the loose number over to the other side.
\[x ^{2} +2x = 3\]
Take half of the coefficient (don't forget the sign!) of the x-term, and square it. Add this square to both sides of the equation
\[x ^{2} + 2x + 1 ^{2} = 3 +1^{2}\]
Convert the left-hand side to squared form, and simplify the right-hand side. (This is where you use that sign that you kept track of earlier. You plug it into the middle of the parenthetical part.)
\[(x+1)^{2} = 4\]
Square-root both sides, remembering the"±" on the right-hand side. Simplify as necessary
\[\sqrt{(x+1)^{2}} = \pm \sqrt{4}\]
\[x+1 = \pm 2\]
\[x = -1\pm2\]
x = -3 or 1