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(a minus sqrtx)^2=25

I have no idea of how to work this problem where i in up with the answers of a=7,-3. Basiclly I just gave it a guess. Could someone show the steps I need to take. Thanks.

  • algebra -

    take the sqrt of each side.

    a-sqrtx=+- 5
    now work each possible sign

    sqrtx=a-5 or sqrt x=a+5

    then square each side:

    x=(a-5)^2 or x=(a+5)^2

    Now you are presented with a quandry, resolve this way. If the domain of x is restricted to real numbers, then you cant take a sqrt of a negative numer, so
    x>= 0 which means
    (a-5)>0 or a>5 and (a+5)>0 a>-5 but the first predominates, so a>5 is the restriction on a.

  • algebra -

    what happen the the results of a=7, -3 to this problem because when I plug them in it equal to 25 in the end. Could you explain this a little more for me. Thanks.

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