Help me understand the meaning of "solve/ find the solution/ what are the roots" using the following?

(x-7) = √ (x-5)

keep in mind that x must be >or= 7 because you are solving for the primary sq.root which must be 0 or positive

square both sides and get

x^2 - 14x + 49 = x - 5

this becomes

x^2 - 15x + 54 = 0

factor and solve

(x - 9)(x - 6) = 0

so x = 9 or x = 6

the only acceptable answer is x = 9 [see above]

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If you substitute these values into the original eqn.

you get

9-7 = sqrt[9-4] so 2 = sqrt[4] is correct and 9 is a solution

6-7 = sqrt[6-5] gives -1 = sqrt[1] which is not correct because sqrt[1] means the primary or positive sqrt which is positive 1 not -1 ............. so 6 is not an acceptable solution

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Obama's certainly not getting a "free pass". The "typical White woman" comment has gotten more media attention than it deserved! I think that characterization was unflattering but not negative and certainly not racist. ridiculous complaining that he is completely unqualified. That seems crazy in light of his years as a legislator, Harvard Law review leadership, community organizer experience, etc. Clearly there are some people who simply prefer another candidate. I have no issue with that. I do have to wonder what's really behind SOME of the rabid anti-Obama wave. Folks who cite his age, his ethnicity, etc for choosing some other candidate are a bit suspect to me. Obama 2008

To solve means to find the unknown value in the given problem.

To find the solution also means the same.

I guess......