4/9w^2 +1 = 5/3w using completing the square method,first re arrange the equation 4/9w^2 -5/3w +1 = 0 to get a whole number, multiply through by 9 4w^2-15w+9=0 next,divide through by the co efficient of w^2 w^2-15/4w+9/4=0 take the constant to the other side 4w^2-15w=-9/4 next, find half of the co efficient of w and add it to both sides w^2-15/4w+(15/8)^2 = (15/8)^2 - 9/4 since the left hand side is a perfect square, it becomes (w+15/8)^2 = (15/8)^2 -9/4. (w+15/8)^2 = 225/64-9/4. (find the lcm of the right hand side ) now square both sides (w+15/8) = squareroot 81/64(squareroot =+_ 9/8) collecting like terms, w= 15/8 +_9/8 w=15+9/8 or w=15-9/8 :.w is either 3 or3/4