To solve this, we have to complete the square of [tex]x^{2} +2x[/tex]To do this with halve the [tex]2x[/tex] and get rid of the x, then get rid of the power on [tex]x^{2}[/tex], and then put them all in brackets, and the square the bracket, like so:[tex]x^{2} +2x[/tex] becomes [tex](x+1)^{2}[/tex]However [tex](x+1)^{2}[/tex] does not equal [tex]x^{2} +2x[/tex] If we expand [tex](x+1)^{2}[/tex] we get [tex]x^{2} +2x + 1[/tex] instead.So to make it equal, all we do is subtract 1.So when we complete the square of [tex]x^{2} +2x[/tex] , we get [tex](x+1)^{2}-1[/tex]---------------------------------------------------------So [tex]x^{2} +2x - 5=0[/tex] becomes:[tex](x+1)^{2}-1-5=0[/tex][tex](x+1)^{2}-6=0[/tex][tex](x+1)^{2}=6[/tex]x + 1 = ±√6x = -1 ± √6______________________________Answer:x = -1 ± √6