SOLUTION: {{{sqrt(4x+1)-sqrt(2x+4)=1}}}

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Question 904562: sqrt%284x%2B1%29-sqrt%282x%2B4%29=1
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%284x%2B1%29-sqrt%282x%2B4%29=1

add sqrt%282x%2B4%29 to both sides of the equation to get:

sqrt%284x%2B1%29 = sqrt%282x%2B4%29%2B1

square both sides of the eqaution to get:

4x%2B1 = 2x+%2B+4+%2B+2%2Asqrt%282x%2B4%29+%2B+1

combine like terms to get:

4x%2B1 = 2x+%2B+5+%2B+2%2Asqrt%282x%2B4%29

subtract 2x and subtract 5 from both sides of the equation to get:

4x+%2B+1+-+2x+-+5 = 2+%2A+sqrt%282x%2B4%29

simplify to get:

2x+-+4 = 2+%2A+sqrt%282x+%2B+4%29

divide both sides of the equation by 2 to get:

x+-+2 = sqrt%282x%2B4%29

square both sides of the equation to get:

%28x-2%29%5E2 = %282x%2B4%29

simplify to get:

x%5E2+-+4x+%2B+4 = 2x+%2B+4

subtract 2x and subtract 4 from both sides of the equation to get:

x%5E2+-+6x = 0

complete the squares to get:

x-3%29%5E2+-+9 = 0

add 9 to both sides of the equation to get:

x-3%29%5E2 = 9

take the square root of both sides of the equation to get:

x-3 = +/- 3

add 3 to both sides of the equation to get:

x = 3+%2B+3 or x = 3+-+3

that makes x = 6 or x = 0

when x = 6, the original equation becomes sqrt%2825%29+-+sqrt%2816%29+=+1 which becomes 5+-+4+=+1 which is true because 1 = 1.

when x = 0, the original equation becomes sqrt%281%29+-+sqrt%284%29+=+1 which becomes 1+-+2+=+1 which is false because -1 does not equal 1.

your solution is therefore that x = 6.