A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sighn0more

  • one year ago

Hello! Please help me work through and solve this problem (it requires the quadratic equation): (3x + 1) ^2 = -2x

  • This Question is Closed
  1. sighn0more
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do I need to expand the binomial first or does this problem require a different course?

  2. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes

  3. sighn0more
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, so that would get me to 9x^2 + 6x + 2 = -2x I think

  4. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[(3x+1)^2=(3x)^2+2(3x)(1)+1^2 \\ (3x+1)^2=9x^2+6x+1\]

  5. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    so should be: \[9x^2+6x+1=-2x \\ \text{ then add } 2x \text{ on both sides } \\ 9x^2+6x+2x+1=0 \\ 9x^2+8x+1=0\]

  6. sighn0more
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh yes, sorry. Error on my part! And from here should these numbers be my values for a, b, and c?

  7. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    yes you can use quadratic formula if you want a=9 b=8 c=1 in the end you should check your answers x being positive will not work just so you know because a real number squared will result in a positive number (or zero) (3x+1)^2=-2x we need x to be negative because 0 obviously doesn't work either

  8. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    and after solving these equation I can tell you you will not have any domain issues with the answers you get

  9. sighn0more
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Perfect! I ended up getting -8 +- radical 28 / 18

  10. sighn0more
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I guess I would need to simplify this further...

  11. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[x=\frac{-8 \pm \sqrt{28}}{18} \\ \text{ note : } \sqrt{28}=\sqrt{4 \cdot 7} =\sqrt{4} \sqrt{7}=2 \sqrt{7} \\ \] yes your solution can be simplified see the note as a hint

  12. sighn0more
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh, so my final answer would be x = -4/9 +- radical 7 / 9

  13. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[x=\frac{-8 \pm 2 \sqrt{7}}{18} \\ \text{ divide \top and bottom by 2 } \\ x=\frac{\frac{-8}{2} \pm \frac{2}{2} \sqrt{7}}{\frac{18}{2}} \\ x=\frac{-4 \pm \sqrt{7}}{9} \\ \text{ yes this could be written as } x=\frac{-4}{9} \pm \frac{\sqrt{7}}{9}\]

  14. sighn0more
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you!!! This helped a bunch.

  15. freckles
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    cool stuff! :)

  16. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.