SOLUTION: sqrt(7x+1)-sqrt(5x+4)=1

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Question 884241: sqrt(7x+1)-sqrt(5x+4)=1
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%287x%2B1%29-sqrt%285x%2B4%29=1
%287x%2B1%29-2sqrt%28%287x%2B1%29%285x%2B4%29%29%2B5x%2B4=1
12x%2B5-2sqrt%28%287x%2B1%29%285x%2B4%29%29=1
12x%2B4=2sqrt%28%287x%2B1%29%285x%2B4%29%29
4%283x%2B1%29=2sqrt%28%287x%2B1%29%285x%2B4%29%29
2%283x%2B1%29=sqrt%28%287x%2B1%29%285x%2B4%29%29
4%289x%5E2%2B6x%2B1%29=35x%5E2%2B33x%2B4
36x%5E2%2B24x%2B4=35x%5E2%2B33x%2B4
x%5E2-9x=0
x%28x-9%29=0
Two solutions:
x=0
and
x-9=0
x=9
Verifying the solutions:
sqrt%287x%2B1%29-sqrt%285x%2B4%29=1
sqrt%287%280%29%2B1%29-sqrt%285%280%29%2B4%29=1
1-2=1
False, not a real solution.
sqrt%287x%2B1%29-sqrt%285x%2B4%29=1
sqrt%287%289%29%2B1%29-sqrt%285%289%29%2B4%29=1
sqrt%2864%29-sqrt%2849%29=1
8-7=1
1=1
True.
highlight_green%28x=9%29

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is:
sqrt(7x+1)-sqrt(5x+4)=1
add sqrt(5x+4) to both sides of the equation to get:
sqrt(7x+1) = 1+sqrt(5x+4)
square both sides of the equation to get:
7x+1 = 1 + 2*sqrt(5x+4) + 5x+4
combine like terms to get:
7x+1 = 2*sqrt(5x+4) + 5x + 5
subtract 5x and 5 from both sides of the equation to get:
2x-4 = 2*sqrt(5x+4)
divide both sides of the equation by 2 to get:
x-2 = sqrt(5x+4)
commute this equation to get:
sqrt(5x+4) = x-2
square both sides of this equation to get:
5x+4 = x^2 -4x + 4
subtract 5x and 4 from both sides of this equation to get:
0 = x^2 - 9x
commute this equation to get:
x^2 - 9x = 0
factor this equation to get:
x * (x-9) = 0
solve for x to get:
x = 0 or x = 9
substitute these answers in the original equation to confirm whether the solutions are good or not.

substituting 0 gets:
sqrt(1) - sqrt(4) = 1 which becomes:
1 - 2 = 1 which becomes:
1 = 3 which is not true, therefore x = 0 is not a solution.

substituting 9 gets:
sqrt(64) - sqrt(49) = 1 which becomes:
8 - 7 = 1 which becomes:
1 = 1 which is true, therefore x = 9 is a solution.

the solution is x = 9.