# Value of x. please check work

1. Jan 15, 2012

### FlopperJr

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
x≥8 and x≥2
I think its just one x≥2

Last edited by a moderator: Jan 16, 2012
2. Jan 15, 2012

### CompuChip

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 $x \ge 2$: 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 $\ge$ sign by a =-sign and solve the equality first. Can you do that for us?

3. Jan 15, 2012

### FlopperJr

then i solve that?

4. Jan 15, 2012

### FlopperJr

I got -8≤x≤-2

5. Jan 16, 2012

### CompuChip

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.

6. Jan 16, 2012

### FlopperJr

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

7. Jan 16, 2012

### FlopperJr

Oops i had my signs reversed but I got the answer now.
x≤-8 x≥-2

8. Jan 16, 2012

### FlopperJr

Thank you so much for your time and help! It means a lot!!

9. Jan 16, 2012

### 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.

10. Jan 16, 2012

### FlopperJr

Ahhhh. I see now, that helps. Thank you!