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boomerang285

  • 2 years ago

sqrt x+10 = x-2

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  1. boomerang285
    • 2 years ago
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    \[\sqrt{x+10}=x-2\]

  2. Nameless
    • 2 years ago
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    you first need to get rid of the radical.

  3. Nameless
    • 2 years ago
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    so square both sides.

  4. boomerang285
    • 2 years ago
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    ok

  5. Nameless
    • 2 years ago
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    so you should have x+10 = x^2-4x-4 ?

  6. Nameless
    • 2 years ago
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    now move your terms all to one side and set it equal to 0 and factor or use the quadratic to solve for x

  7. boomerang285
    • 2 years ago
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    ok

  8. Nameless
    • 2 years ago
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    actualy... i typoed.. it should be \[x+10=x^{2}-4x+4\]

  9. boomerang285
    • 2 years ago
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    ok i was confused trying to work that out

  10. Nameless
    • 2 years ago
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    and the only reason i move to the right is cause I dont want to multiply by a negative 1.

  11. Nameless
    • 2 years ago
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    \[x ^{2}-5x-6=0\]

  12. Nameless
    • 2 years ago
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    you know how to factor or do the quadratic?

  13. boomerang285
    • 2 years ago
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    i have my text book here, these confuse me so much

  14. Nameless
    • 2 years ago
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    ok. i would factor this. so you set up parens.. ( )( ) right? fill them with (x )(x ). now we are looking for 2 numbers that multiply to 6 and add to -5

  15. Nameless
    • 2 years ago
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    so 2 and 3 seem to work nice.. but they are not gonna get us to where we want because of the negative 5. so we try 1 and 6. (x 1)(x 6) right?

  16. boomerang285
    • 2 years ago
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    so 2 and 3

  17. boomerang285
    • 2 years ago
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    ok

  18. Nameless
    • 2 years ago
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    now since we know we a negative 5.. we know that 6 has to be negative. so (x+1)(x-6)

  19. boomerang285
    • 2 years ago
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    so (x+1)(x-6)

  20. Nameless
    • 2 years ago
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    solve those as separate equations .. x-6=0 and x+1=0

  21. boomerang285
    • 2 years ago
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    x=6 x=-1

  22. Nameless
    • 2 years ago
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    yep. now.. the most important.. you need to plus these numbers back into the equation.. to check if both answers work.

  23. boomerang285
    • 2 years ago
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    ok

  24. Nameless
    • 2 years ago
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    \[\sqrt{-1+10} =-1 - 2\]

  25. Nameless
    • 2 years ago
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    \[\sqrt{6+10} = 6-2\]

  26. boomerang285
    • 2 years ago
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    sqrt9=-3 sqrt16 = 4

  27. Nameless
    • 2 years ago
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    so x = 6 is your only answer? does that make sense?

  28. Nameless
    • 2 years ago
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    \[\sqrt{9} =3 \neq -1-2 = -3\] \[\sqrt{16}=4 = 6-2=4\]

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