he sum of a number and its positive square root is 6/25. Find the number
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Let the number be n^2. So
n^2 + n = 6/25, or
25 n^2 + 25 n = 6, or
25 n^2 + 25 n - 6 = 0
The product of 25 and -6 = -150. Its factors are +30 and -5. So we re-write the equation as
25 n^2 + 30 n - 5 n - 6 = 0, or
5n (5n +6) - 1*(5n + 6) = 0, or
(5n - 1)(5n +6) = 0
Therefore n = 1/5 or -6/5.
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