SOLUTION: Solve {{{sqrt(x+2)+sqrt(3x+4)=2}}}

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Question 742830: Solve
sqrt%28x%2B2%29%2Bsqrt%283x%2B4%29=2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B2%29%2Bsqrt%283x%2B4%29=2.....square both sides

%28sqrt%28x%2B2%29%2Bsqrt%283x%2B4%29%29%5E2=2%5E2

x%2B2%2B2%2Asqrt%28x%2B2%29sqrt%283x%2B4%29%2B3x%2B4=4
4x%2B6%2B2%2Asqrt%28x%2B2%29sqrt%283x%2B4%29=4
2%2Asqrt%28x%2B2%29sqrt%283x%2B4%29=-4x-6%2B4
2%2Asqrt%28x%2B2%29sqrt%283x%2B4%29=-4x-2
%282%2F2%29%2Asqrt%28x%2B2%29sqrt%283x%2B4%29=-4x%2F2-2%2F2
sqrt%28%28x%2B2%29%283x%2B4%29%29=-2x-1...square both sides
%28sqrt%28%28x%2B2%29%283x%2B4%29%29%29%5E2=%28-2x-1%29%5E2
%28x%2B2%29%283x%2B4%29=%28-2x%29%5E2-2%2A2x%28-1%29%2B1
3x%5E2%2B4x%2B6x%2B8=4x%5E2%2B4x%2B1
4x%5E2-3x%5E2-10x-8%2B4x%2B1=0
x%5E2-6x-7=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%2A1%2A%28-7%29+%29%29%2F%282%2A1%29+
x+=+%286+%2B-+sqrt%28+36%2B28+%29%29%2F2+
x+=+%286+%2B-+sqrt%28+64%29%29%2F2+
x+=+%286+%2B-+8%29%2F2+
solutions:
x+=+%286+%2B8%29%2F2+
x+=+7+.........this solution doesn't work
or
x+=+%286+-8%29%2F2+
x+=+-1+........only this solution does work; so, this is your answer