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Value of x. please check work

  1. Jan 15, 2012 #1
    1. The problem statement, all variables and given/known data

    determine the values of x for which x2+10x+38≥22

    2. Relevant equations

    -b/2a I put into complete square.
    the previous question in part a asked me to write the equation in the form (x+b)2+c
    For that I got (x-5)2+13

    3. The attempt at a solution
    (x-5)2+13 ≥ 22
    add 13 to both sidesthen square root both sides
    and i got x-5 ≥±3
    then add 5
    so i get 2 answers??
    x≥8 and x≥2
    I think its just one x≥2
     
    Last edited by a moderator: Jan 16, 2012
  2. jcsd
  3. Jan 15, 2012 #2

    CompuChip

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    Science Advisor
    Homework Helper

    Did you actually check the result of (x - 5)2 + 13? You might find that you need to change some signs.
    Also you said you add 13, where you should have subtracted (though according to the formula you did it right).

    One of the very first things when working with functions is that you should make a plot, or at least a sketch. Can you draw the functions y = x2 + 10x + 38 and y = 22? Now check your answer [itex]x \ge 2[/itex]: does it look correct to you?

    Please note that in general, you shouldn't just solve inequalities like they are equalities. What you normally do, is replace the [itex]\ge[/itex] sign by a =-sign and solve the equality first. Can you do that for us?
     
  4. Jan 15, 2012 #3
    Okay thanks for your reply. I assume it should be (x+5)^2+13=22
    then i solve that?
     
  5. Jan 15, 2012 #4
    I got -8≤x≤-2
     
  6. Jan 16, 2012 #5

    CompuChip

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    Did you assume that, or are you sure? (You can work out the brackets and simplify, you should get x2 + 10x + 38 back).

    Yep

    Does that agree with the sketch you drew?
    Note that if you get x = -2 and x = -8 you will need to check the three regions x < -2, -2 < x < -8 and x > -8 separately (either by looking at the graph or by plugging in a number from the region) to see which way the inequality holds.
     
  7. Jan 16, 2012 #6
    Okay, Thanks. But I'm still not understanding. Once I do that, If it matches will i just keep that answer. Also will they have to be seperate.

    x≥-8 and x≤-2
     
  8. Jan 16, 2012 #7
    Oops i had my signs reversed but I got the answer now.
    x≤-8 x≥-2
     
  9. Jan 16, 2012 #8
    Thank you so much for your time and help! It means a lot!!
     
  10. Jan 16, 2012 #9

    Mark44

    Staff: Mentor

    That's not how it works. You should never end up with ± in an inequality.

    Here's a simpler example.

    If (x -1)2 >= 9,
    then x - 1 >= 3 or x - 1 <= -3
    so x >= 4 or x <= -2.

    Your textbook probably has some more examples.
     
  11. Jan 16, 2012 #10
    Ahhhh. I see now, that helps. Thank you!
     
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