Question

How to complete the squarela1" title=" {x}^{2} - 2x - 8 = 0" alt=" {x}^{2} - 2x - 8 = 0" align="absmiddle" class="latex-formula">

Answer 1

$(a-b)^2=a^2-2ab+b^2\qquad(*)\\\\x^2-2x-8=0\qquad|\text{add 8 to both sides}\\\\x^2-2x\cdot1=8\qquad|\text{add}\ 1^2\ \text{to both sides}\\\\\underbrace{x^2-2(x)(1)+1^2}_{(*)}=8+1^2\\\\(x-1)^2=9\iff x-1=\pm\sqrt9\\\\x-1=-3\ \vee\ x-1=3\qquad|\text{add 1 to both sides}\\\\x=-2\ \vee\ x=4$