Final answer:
To find the sum of all solutions to the equation w = sqrt(108w), square both sides of the equation to eliminate the square root. The solutions are then found by setting the factors equal to zero, giving us w = 0 and w = 108. The sum of all solutions is 108.
Step-by-step explanation:
In order to find the sum of all solutions to the equation w = sqrt(108w), we need to solve the equation first. To do this, we can square both sides of the equation to eliminate the square root. This gives us w^2 = 108w. We can then rearrange the equation to w^2 - 108w = 0. Next, we factor out w from the equation to get w(w - 108) = 0. Setting each factor equal to zero gives us two possible solutions: w = 0 and w = 108.
Therefore, the sum of all solutions to the equation is 0 + 108 = 108.