Completing the square and area

Use the slider bars to set the values of [math]a[/math] then [math]b[/math] in the equation [math]x^{2} + ax = b[/math].[br]How do you know that the blue regions in each diagram have equal area?[br]How do you know that the shape on the right is square?[br]How do you find the area of the yellow region?[br]Why is this process called COMPLETING THE SQUARE? [br]How is the process of completing the square helpful to solve the equation?

Information: Completing the square and area