A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

How do you complete the square to form perfect trinomial for 4x^2=14x+8

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

    x=4, -1/2

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

    How did you do it tho steps pleases

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

    1 Move all terms to one side 4x2−14x−8=0 2 Factor out the common term 2 2(2x2−7x−4)=0 3 Factor 2x2−7x−4 1. Multiply 2 by -4, which is -8. 2. Ask: Which two numbers add up to -7 and multiply to -8? 3. Answer: 1 and -8 4. Rewrite −7x as the sum of x and −8x: 2(2x2+x−8x−4)=0 4 Factor out common terms in the first two terms, then in the last two terms 2(x(2x+1)−4(2x+1))=0 5 Factor out the common term 2x+1 2(2x+1)(x−4)=0 6 Solve for x 1. Ask: When will (2x+1)(x−4) equal zero? 2. Answer: When 2x+1=0 or x−4=0. 3. Solve each of the 2 equations above: x=−12,4

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

    fan and medal please

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

    how do I do that

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

    fan me, go to my name and something will come and it says 'become a fan', and click that

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

    Thanks lol can you also help me with others?

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

    sure

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

    4x^2+5X+2=0

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

    Also on the first one how did you get -12,4 but you said it's 4,1/2

  11. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    He got -1/2 and 4. He just forgot to write the / between the -1 and the 2.

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

    ohh okay thank you!!

  13. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Do you just need to solve the equation using any method, or do you have to use the complete the square method?

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

    it just says complete the square to form a perfect square trinomial

  15. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Then you need to complete the square. This is how you complete the square to solve a quadratic equation. I'll show you the steps.

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

    thank your a life saver!

  17. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Your equation is: \(4x^2=14x+8\) 1. You need the x^2 term and the x term to the left side, and the number on the right side. All we need to do is subtract 14x from both sides. \(4x^2 - 14x = 8\)

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

    wait so idont have to have the 4,1/2

  19. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2. The first term must be just x^2 (without a coefficient). If it is not, then divide both sides of the equation by the coefficient of the x^2 term. In our case, we divide the equation by 4 on both sides to get: \(\dfrac{4}{4}x^2 - \dfrac{14}{4}x = \dfrac{8}{4} \) which simplifies to \(x^2 - \dfrac{7}{2}x = 2 \) As you can see, we now have just x^2 for the x^2 term.

  20. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    4 and -1/2 are the solutions of the equation. If we complete the square and continue, we will get to 4 and -1/2. You'll see.

  21. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now we are just completing the square.

  22. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    We are ready for the next step. This is the actual step that completes the square.

  23. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    3. Take half of the coefficient of the x-term, and square it. Add it to both sides. \(x^2 - \dfrac{7}{2}x = 2 \) Half of 7/4 is 7/4. The square of 7/4 is 49/16. We add 49/16 to both sides. \(x^2 - \dfrac{7}{2}x + \dfrac{49}{16} = 2 + \dfrac{49}{16} \) Now we write the left side as the square of a binomial, and we add the fractions on the right side.

  24. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \(\left(x - \dfrac{7}{4} \right)^2 = \dfrac{32}{16} + \dfrac{49}{16} \) \(\left(x - \dfrac{7}{4} \right)^2 = \dfrac{81}{16} \) Ok, the complete the square step is finished.

  25. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    If all you need to do is complete the square, you are done now.

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

    im so confused lol

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

    is that a perfect square trinomial?

  28. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Yes. The left side is a perfect square trinomial when written as \(x^2 - \dfrac{7}{2}x + \dfrac{49}{16} \)

  29. mathstudent55
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Once you complete the square, you can solve the quadratic equation. Take square roots of both sides: \(\sqrt{\left(x - \dfrac{7}{4} \right)^2} = \pm \sqrt{\dfrac{81}{16}} \) \(x - \dfrac{7}{4} = \pm\dfrac{9}{4} \) Now separate the equation into two equations: \(x - \dfrac{7}{4} = \dfrac{9}{4} \) or \(x - \dfrac{7}{4} = -\dfrac{9}{4} \) \(x = \dfrac{9}{4} + \dfrac{7}{4} \) or \(x = - \dfrac{9}{4} +\dfrac{7}{4} \) \(x = \dfrac{16}{4} \) or \(x = - \dfrac{2}{4}\) \(x = 4\) or \(x = -\dfrac{1}{2} \) As you can see, we get x = 4 or x = -1/2, as you had gotten before.

  30. 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.