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
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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) (Show Source): You can put this solution on YOUR website!
You can just use sqrt(10-2x) to denote the square root function.
.
.
.
Square both sides.
Square both sides again,
Two solutions:
.
.
.
.
.
.
Verify the solutions,
Since would lead to a negative argument for the square root function, it is not a solution.
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.
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Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
You seem to have the right idea, will go thru it step by step:
= 3
:
= + 3; I think you have the wrong sign here
:
Square both sides, FOIL the right side
10 - 2x = (5x+16) + + 9
:
10 - 2x = 5x + 25 +
:
10 - 25 - 2x - 5x =
:
-7x - 15 =
:
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
:
:
two solutions
x =
x = +2.387755
and
x =
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.
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