Algebra

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deepoe: Master | Next Rank: 500 Posts; Posts: 151; Joined: Wed Feb 11, 2009 2:45 am; Thanked: 3 times

by deepoe » Fri Feb 13, 2009 4:16 pm

Could someone solve this problem?

(x^2+6x+9) + 6(x+3) + 9 = 0

I didn''t got further till this:

(x^2+6x+9) + 6x = - 27

What's the next step I need to take? Open the square?

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Source: Beat The GMAT — Problem Solving | Fri Feb 13, 2009 4:16 pm

truplayer256: Master | Next Rank: 500 Posts; Posts: 392; Joined: Thu Jan 15, 2009 12:52 pm; Location: New Jersey; Thanked: 76 times

by truplayer256 » Fri Feb 13, 2009 4:35 pm

(x+3)^(2)+6(x+3)+9=0
(x+3)[(x+3)+6]=-9
(x+3)(x+9)=-9
x^2+12x+27=-9
x^2+12x+36=0
(x+6)^(2)=0
x+6=0
x=-6

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jhhatdaddy: Newbie | Next Rank: 10 Posts; Posts: 6; Joined: Thu Jan 08, 2009 6:36 pm

by jhhatdaddy » Sat Feb 14, 2009 4:38 am

isnt it even easier than that?

(x^2+6x+9) + 6(x+3) + 9 = 0

x^2+6x+9+6x+18+9=0
x^2+12x+36-0
(x+6)^2=0

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deepoe: Master | Next Rank: 500 Posts; Posts: 151; Joined: Wed Feb 11, 2009 2:45 am; Thanked: 3 times

by deepoe » Sat Feb 14, 2009 6:07 am

truplayer256 wrote:(x+3)^(2)+6(x+3)+9=0
(x+3)[(x+3)+6]=-9
(x+3)(x+9)=-9
x^2+12x+27=-9
x^2+12x+36=0
(x+6)^(2)=0
x+6=0
x=-6

Did you divide the (x+3) from 6(x+3) ?

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Etoiles: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Sun Feb 08, 2009 3:53 pm

what to do next

by Etoiles » Sat Feb 14, 2009 10:12 am

2 ways
either develop as and solve
or recognize that X^2 +6X+9 is (X+3)^2
and factorize x+3 and then solve
and refactorize x+6 Recognizing that X^2 +12X+36
is (X+6 ) ^2

ps it is the formula (a+b)^2 = a^2 +b^2+2ab

hope it helps

when there is a will there is a way ... believe in yourself ... kind regards

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deepoe: Master | Next Rank: 500 Posts; Posts: 151; Joined: Wed Feb 11, 2009 2:45 am; Thanked: 3 times

by deepoe » Mon Feb 16, 2009 2:24 am

Thanks but what do you do with the ^2?

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