Develop a geometric argument to solve ‘a square is equal to things and numbers, that is, an equation of the form x^2 = bx + c.”
I need to geometrically justify the quadratic formula that solves x^2-bx=c, which gives x=sqrt((b/2)^2+c))+(b/2). The textbook describes the procedure when it is x^2+bx=c as adding a multiple of a side to an area with the multiple being a rectangle of length x and width b, a rectangle that is added to a square of side x. They then describe it as cutting half the rectangle off from one side of the square and putting it on the bottom and adding a square of side b/2 to complete the square. So then x's length is described by the formula.
It then says; however, that when it is x^2-bx=c, it is more complicated and not alike. Please help. Thanks.