The sum of a number and its positive square root is 6/25.find the number.

quadratic equation sum

Let the number be x.
Thus, its square root will be sqrt(x).

Since their sum is 6/25, we have:
x + sqrt(x) = 6 / 25
sqrt(x) = (6 / 25) - x
(sqrt(x))^2 = ((6 / 25) - x)^2
x = (36 / 625) - (12 / 25)x + x^2
625x = 36 - 300x + 625x^2
625x^2 - 925x + 36 = 0

Using the quadratic formula, we have:
x = [925 +/- sqrt((-925)^2 - 4(625)(36))] / [2(625)]
x = [925 +/- sqrt(765625)] / 1250
x = [925 +/- 875] / 1250
x = 1800 / 1250 or x = 50 / 1250
x = 36 / 25 or x = 1 / 25

Notice that 36 / 25 + sqrt(36 / 25) does not give you 6 / 25.
Thus, we can reject it, and the only solution is 1 / 25