Suppose we use x to represent the width of the rectangle in feet. The equation for the area of the rectangle can be written as
66 = x(2x+1)
2x^2 + x - 66 = 0 (subtract 66, put in standard form)
x = (-1 ± √(1^2 - 4(2)(-66)))/(2(2)) (use the quadratic formula)
x = (-1 ± √529)/4 (simplify)
x = (-1 ± 23)/4 (simplify)
x = {-6, 11/2} (find the two solutions)
Only the positive solution makes sense as a dimension. The width (x) is 5.5 ft; the length (2x+1) is 12 ft.
66 = x(2x+1)
2x^2 + x - 66 = 0 (subtract 66, put in standard form)
x = (-1 ± √(1^2 - 4(2)(-66)))/(2(2)) (use the quadratic formula)
x = (-1 ± √529)/4 (simplify)
x = (-1 ± 23)/4 (simplify)
x = {-6, 11/2} (find the two solutions)
Only the positive solution makes sense as a dimension. The width (x) is 5.5 ft; the length (2x+1) is 12 ft.
