I have a question regarding this problem below? I noticed it in an eariler post, and have come to figure that my text book has it like this? What would be the solution for this?
x+sqrt(11-x)= 5
x = 2? OR 2,7? OR NO solution?
I say x = 2 only? Any Thoughts?
x=2
x=7 the way I see it.
Rewrite it as
sqrt(11-x)=5-x and solve
The way it is written is
x+sqrt(11-x)= 5
x+ sqrt sign11-x = 5
the x is under the root sign then = 5
Would this still have the same conclusion? 2,7, or just 2 ?
I solve it this way.
x+sqrt(11-x)=5
sqrt(11-x) = 5-x
square both sides
11-x = 25-10x+x^2
move everything to the right.
25-10x+x^2-11+x
combine terms
0=14-9x+x^2
rearrange just for convenience.
x^2-9x+14=0
factor to
(x-7)(x-2)=0
x=7
x=2
Check my work.
I ran this through an equation solver and it it tells me x = 2 only?
I seem to remember in the dim dark past something about squaring introducing a false root; however, I'm not up enough on this to answer as an expert in the subject. I have two suggestions:
1. I can delete my answers, leave your post, and perhaps another tutor will straighten it out, OR
2. We can leave everything and hope another tutor reads this and chimes in. Your choice but I think your best choice is #1 because sometimes others don't check a problem if it has been answered.
Dr. Bob and Mr. Bob agree on the (C) 2,7 as the mathematically correct solution.
The reason that your equation solver gives you only 2 is most probably the same reason why a calculator gives you 2 as a square root of 4, without giving you -2 as an option. It processed the positive square-root only.
See also discussions in:
http://www.jiskha.com/display.cgi?id=1249274152
Thanks. I needed that.
ok hunny so you need some help let me see babe. i think that it is x=2
i hope i have helped you hunny xx
To solve the equation x + sqrt(11 - x) = 5, you need to isolate the variable x on one side of the equation. Here's how you can solve it step by step:
1. Start by subtracting x from both sides of the equation to eliminate it from the square root term:
x + sqrt(11 - x) - x = 5 - x
sqrt(11 - x) = 5 - x
2. Next, square both sides of the equation to eliminate the square root:
(sqrt(11 - x))^2 = (5 - x)^2
11 - x = 25 - 10x + x^2
3. Rearrange the equation and simplify:
x^2 - 9x + 14 = 0
4. Factor the quadratic equation:
(x - 2)(x - 7) = 0
5. Set each factor equal to zero and solve for x:
x - 2 = 0 --> x = 2
x - 7 = 0 --> x = 7
By solving the quadratic equation, you find that x could be equal to either 2 or 7.
Therefore, the solutions to the equation x + sqrt(11 - x) = 5 are x = 2 and x = 7.