SOLUTION: I having trouble getting this radical expression to solve. I do not have the root symbol so I will use the forward slash. I get different answers each time I try to solve. Can you

Algebra ->  Radicals -> SOLUTION: I having trouble getting this radical expression to solve. I do not have the root symbol so I will use the forward slash. I get different answers each time I try to solve. Can you       Log On


   

Question 372500: I having trouble getting this radical expression to solve. I do not have the root symbol so I will use the forward slash. I get different answers each time I try to solve. Can you please help me understand this problem?
/10 − 2x − /5x + 16 = 3
/10-2x=3-/5x+16
(/10-2x)^2= (3- /5x+16)^2
10-2x=9-6/5x+16 + (5x+16)
10=9-6/5x+16
1=6/5x+16
0.1666=/5x+16
0.1666^2=(/5x+16)^2
0.03=5x+256
-255.973 or -256=x
Found 2 solutions by Fombitz, ankor@dixie-net.com:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You can just use sqrt(10-2x) to denote the square root function.
.
.
.
sqrt%2810-2x%29-sqrt%285x%2B16%29=3
sqrt%2810-2x%29=sqrt%285x%2B16%29%2B3
Square both sides.
10-2x=5x%2B16%2B6%2Asqrt%285x%2B16%29%2B9
10-2x=5x%2B25%2B6%2Asqrt%285x%2B16%29
-15-7x=6%2Asqrt%285x%2B16%29
-%287x%2B15%29=6%2Asqrt%285x%2B16%29
Square both sides again,
49x%5E2%2B210x%2B225=36%285x%2B16%29
49x%5E2%2B210x%2B225=180x%2B576%29
49x%5E2%2B30x-351=0
%2849x-117%29%28x%2B3%29=0
Two solutions:
49x-117=0
x=117%2F49
.
.
.
x%2B3=0
x=-3
.
.
.
Verify the solutions,
Since x=117%2F49 would lead to a negative argument for the square root function, it is not a solution.
highlight%28x=-3%29
.
.
.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
You seem to have the right idea, will go thru it step by step:
sqrt%2810+-+2x%29+-+sqrt%285x+%2B+16%29 = 3
:
sqrt%2810+-+2x%29 = sqrt%285x+%2B+16%29 + 3; I think you have the wrong sign here
:
Square both sides, FOIL the right side
10 - 2x = (5x+16) + 6sqrt%285x+%2B+16%29 + 9
:
10 - 2x = 5x + 25 + 6sqrt%285x+%2B+16%29
:
10 - 25 - 2x - 5x = 6sqrt%285x+%2B+16%29
:
-7x - 15 = 6sqrt%285x+%2B+16%29
:
square again, FOIL the left side
49x^2 + 105x + 105x + 225 = 36(5x + 16)
:
49x^2 + 210x + 225 = 180x + 576
:
Combine on the right
49x^2 + 210x - 180x + 225 - 576 = 0
;
A quadratic equation
49x^2 + 30x - 351 = 0
:
Use the quadratic formula to find x. a=49; b=30; c=-351
x+=+%28-30+%2B-+sqrt%2830%5E2-4%2A49%2A-351+%29%29%2F%282%2A49%29+
:
x+=+%28-30+%2B-+sqrt%28900-%28-68796%29+%29%29%2F98+
:
x+=+%28-30+%2B-+sqrt%2869696+%29%29%2F98+
two solutions
x+=+%28-30+%2B+264%29%2F98+
x = 234%2F98
x = +2.387755
and
x+=+%28-30+-+264%29%2F98+
x = %28-294%29%2F98
x = -3
:
I checked both these solutions in the original problem. You can confirm this yourself, however.
:
I'm not surprised that you had difficulty, a dozen ways to go wrong here.