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anonymous

  • one year ago

Solve by completing the square x^2-20x+30=0

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  1. KaiserTheSlayer
    • one year ago
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    using this would help you and remember the a=1, b=-20, and c=30

  2. anonymous
    • one year ago
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    \[x^2-2*x*10+10^2-10^2+30=0\]

  3. anonymous
    • one year ago
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    what do you do after that? @surjithayer

  4. anonymous
    • one year ago
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    do i used the quadratic formula to solve by completing squares? @KaiserTheSlayer

  5. KaiserTheSlayer
    • one year ago
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    yes

  6. KaiserTheSlayer
    • one year ago
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    so it would be x=18.36660026534076 and x= 1.63339973465925

  7. anonymous
    • one year ago
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    oh okay thank you

  8. KaiserTheSlayer
    • one year ago
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    yup

  9. ChillOut
    • one year ago
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    Solving by square completion yields:\[x²-20x=-30\]\[x²-20x + 100 = 70\]\[(x-10)²=70\] There you have it. Do you the step-by-step?

  10. anonymous
    • one year ago
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    no i don't

  11. anonymous
    • one year ago
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    \[(x-10)^2-100+30=0\] \[\left( x-10 \right)^2=70=\left( \sqrt{70} \right)^2\] \[x-10=\pm \sqrt{70}\] x=?

  12. anonymous
    • one year ago
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    where is the 100 coming from?

  13. ChillOut
    • one year ago
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    You take half of the x coefficient, square it and add to both sides.

  14. anonymous
    • one year ago
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    thats right! i sorta remember now

  15. ChillOut
    • one year ago
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    Don't forget to divide everything by whatever is multiplying the squared term ;). In this case, it's "1", so it won't matter.

  16. anonymous
    • one year ago
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    so then to figure out what x is I solve... x-10=\[\sqrt{70}\] and x-10=\[\sqrt{-70}\]

  17. anonymous
    • one year ago
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    idk why it looks like that i was trying to write what you did on the last thing

  18. ChillOut
    • one year ago
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    Be careful! The second solution you gave is a COMPLEX number.

  19. anonymous
    • one year ago
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    i know i have to do the whole i stuff for that cause its a negative square root

  20. ChillOut
    • one year ago
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    No, it's not:\[x-10=\sqrt{70} \]or\[x-10=-\sqrt{70}\]

  21. ChillOut
    • one year ago
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    notice the minus sign is outside.

  22. anonymous
    • one year ago
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    yeah i see that now

  23. ChillOut
    • one year ago
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    And that's it! you have your solutions! Just move the independent term to the other side.

  24. anonymous
    • one year ago
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    yeah i got it now, thank you!

  25. ChillOut
    • one year ago
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    The whole thing about completing the square is to make the left side equation look like something like (x-a)² or (x+a)²

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