Question

solve 4x^2+4bx-(a^2-b^2) by the method of completing the square

Answer 1

4x^2 +4bx-(a+b)(a-b)=4x^2+2x{(a+b)-(a-b)}-(a-b)(a-b)=4x^2+2x(a+b)-2x(a-b)-(a+b)(a-b)=2x{2x+(a+b)}-(a-b){2x+(a+b)}={2x+(a+b)}{2x-(a-b)}= so x=-(a+b)/2 and x=a-b/2