[tex]Use\ (a+b)^2=a^2+2ab+b^2\qquad(*).\\\\x^2+2x-7=17\qquad\text{add 7 to both sides}\\\\x^2+2(x)(1)=24\qquad\text{add}\ 1^2\ \text{to both sides}\\\\\underbrace{x^2+2(x)(1)+1^2}_{use\ (*)}=24+1^2\\\\(x+1)^2=25\iff x+1=\pm\sqrt{25}\\\\x+1=-5\ \vee\ x+1=5\qquad\text{subtract 1 from both sides}\\\\\boxed{x=-6\ \vee\ x=4}[/tex]
