SOLUTION: The sum of twice a number and 1 is equal to 3 times the positive square root of the number. Find the number. Write an equation and solve.

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Question 628095: The sum of twice a number and 1 is equal to 3 times the positive square root of the number. Find the number. Write an equation and solve.
Answer by mananth(16946) About Me  (Show Source):
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The sum of twice a number and 1 is equal to 3 times the positive square root of the number. Find the number. Write an equation and solve.
Let the number be x
2x%2B1+=+3sqrt%28x%29
square both sides
%282x%2B1%29%5E2+=+%283sqrt%28x%29%29%5E2

4x%5E2%2B4x%2B1=+9x
4x%5E2-5x%2B1=0
4x%5E2-4x-x%2B1=0
4x%28x-1%29%2B1%28x-1%29=0
(x-1)(4x-1)=0
either x-1 = 0 or 4x-1 =0
if x-1 =0
x= 1
if 4x-1 =0 then
4x=1
x= 1/4
x= 1OR 1/4