SOLUTION: Hello, could you please help me solve this equation. I initially tried solving by squaring both sides but the result seemed to be something awful. When I subtracted 4 from both s

Algebra ->  Radicals -> SOLUTION: Hello, could you please help me solve this equation. I initially tried solving by squaring both sides but the result seemed to be something awful. When I subtracted 4 from both s      Log On


   

Question 359732: Hello, could you please help me solve this equation. I initially tried solving by squaring both sides but the result seemed to be something awful. When I subtracted 4 from both sides and then squared both sides, my answer was x = 15/4
This is the equation:
4 + sqrt(10-x) = 6 + sqrt(4-x) solve for x
thank you.
Found 2 solutions by solver91311, Fombitz:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


You are spot on. Here's how I know (aside from solving the problem myself)



Just do the arithmetic. If you get a true statement, then is an element (and as it turns out the only element) of the solution set.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2810-x%29+=+2+%2B+sqrt%284-x%29
10-x=4%2B4sqrt%284-x%29%2B%284-x%29
10-x=8-x%2B4sqrt%284-x%29
2=4sqrt%284-x%29
4=16%284-x%29
4=64-16x
16x=60
x=60%2F16
highlight%28x=15%2F4%29
Me too, well done.
You can always verify your answer by sticking it back in the equation.
4+%2B+sqrt%2810-15%2F4%29+=+6+%2B+sqrt%284-15%2F4%29++
4%2Bsqrt%28%2840-15%29%2F4%29=6%2Bsqrt%2816%2F4-15%2F4%29
4%2Bsqrt%2825%2F4%29=6%2Bsqrt%281%2F4%29
4%2B5%2F2=6%2B1%2F2
8%2F2%2B5%2F2=12%2F2%2B1%2F2
13%2F2=13%2F2
True, so the solution is verified.
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