Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

countonme123

  • 3 years ago

Solve quadratic equation by completing the square. Check both roots. problem below

  • This Question is Closed
  1. countonme123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[2x^2-12x +16=0\]

  2. countonme123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    please explain each step I am having trouble with it

  3. Sonita
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2(x^2-6x+8)=0 2[(x-4)(x-2)]=0

  4. countonme123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    please do explain why you do each step

  5. NotTim
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    1st step- Factor out 2. Second step- What 2 numbers add to the end value, and multiply to the middle value?

  6. NotTim
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Those 2 values are then put into the brackets as you see them.

  7. NotTim
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    And here, the signs of positive and negatives are reversed because when you solve for x individually, x-4=0 x=4. Ok?

  8. countonme123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok but there is supposed to be two answers

  9. countonme123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4 is one of them

  10. petewe
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1339466532153:dw|

  11. petewe
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1339466562615:dw|

  12. petewe
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1339466604939:dw|

  13. NotTim
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    eh, you might be might be making this more difficult than it actually is

  14. petewe
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I did what the question asked. Solve quadratic equation by completing the square.

  15. NotTim
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ay. missed that. thx.

  16. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You made a small mistake. The -8 should also be multiplied by -2.

  17. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just 2 rather.

  18. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Leaving you with\[2(x^2-6x+9-9+8)=2((x-3)^2-1)=2(x-3)^2-2\]

  19. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Set equal to 0, and get \[2(x-3)^2-2=0\implies(x-3)^2=1\]Take the root, and solve. \[x-3=\pm1\implies x=4\quad\text{or}\quad x=2\]

  20. countonme123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok george you are right now can you explain each step

  21. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The hardest part is the first couple steps. You start with \[2x^2-12x+16=2(x^2-6x+8)\]The next part is where you complete the square. You take half of \(-6\), square it, and then add/subtract it. So you get\[2(x^2-6x+8)=2(x^2-6x+\left(\frac{-6}{2}\right)^2-\left(\frac{-6}{2}\right)^2+8=2(x^2-6x+9-9+8)\]

  22. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now you simplify as I described before. It's important that you simplify \[x^2-6x+9-9+8\]as \((x-3)^2-1\). That's the whole point of completing the square. You add/subtract just the right amount so you can have the square of a binomial. From there, you can solve for that square easily, and then just take a square root.

  23. KingGeorge
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Did this make sense?

  24. countonme123
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes thank you but please view my next question

  25. 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