SOLUTION: Please help me solve the radical equation: sqrt (x+2) + sqrt (3x+7) = 1

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Question 758352: Please help me solve the radical equation: sqrt (x+2) + sqrt (3x+7) = 1
Found 2 solutions by tommyt3rd, MathLover1:
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
%0D%0Asqrt+%28x%2B2%29+%2B+sqrt+%283x%2B7%29+=+1%0D%0A


%0D%0Asqrt+%28x%2B2%29%5E2++=+%281-sqrt+%283x%2B7%29%29%5E2%0D%0A

%0D%0Ax%2B2=1-2+sqrt%283x%2B7%29%2B3x%2B7%0D%0A


%0D%0A2x%2B6=2sqrt+%283x%2B7%29%0D%0A


%0D%0Ax%2B3=-sqrt%283x%2B7%29%0D%0A



%0D%0A%28x%2B3%29%5E2=%28-sqrt%283x%2B7%29%29%5E2%0D%0A

%0D%0Ax%5E2%2B6x%2B9=3x%2B7%0D%0A

%0D%0Ax%5E2%2B3x%2B2=0%0D%0A



x%5B1%5D=-2

x%5B2%5D=-1 (extraneous)

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

sqrt+%28x%2B2%29+%2B+sqrt+%283x%2B7%29+=+1....square both sides



x%2B2+%2B+2sqrt%28%28x%2B2%29%283x%2B7%29%29%2B3x%2B7+=+1
2sqrt%28%28x%2B2%29%283x%2B7%29%29%2B4x%2B9+=+1
2sqrt%28%28x%2B2%29%283x%2B7%29%29=-4x-9%2B+1
2sqrt%28%28x%2B2%29%283x%2B7%29%29=-4x-8
2sqrt%28%28x%2B2%29%283x%2B7%29%29%2F2=-4x%2F2-8%2F2
sqrt%28%28x%2B2%29%283x%2B7%29%29=-2x-4...square both sides
%28sqrt%28%28x%2B2%29%283x%2B7%29%29%29%5E2=%28-2x-4%29%5E2
%28x%2B2%29%283x%2B7%29=4x%5E2%2B16x%2B16
3x%5E2%2B7x%2B6x%2B14=4x%5E2%2B16x%2B16
3x%5E2%2B13x%2B14=4x%5E2%2B16x%2B16
0=4x%5E2-3x%5E2%2B16x-13x%2B16-14
x%5E2%2B3x%2B2=0...write 3x as 2x%2Bx
x%5E2%2B2x%2Bx%2B2=0.....group
%28x%5E2%2Bx%29%2B%282x%2B2%29=0
x%28x%2B1%29%2B2%28x%2B1%29=0
%28x%2B1%29%28x%2B2%29=0.......use zero product rule
if x%2B1=0 => x=-1
if x%2B2=0 => x=-2
only solution that works is highlight%28x=-2%29 because it makes term sqrt+%28x%2B2%29 equal to zero and term sqrt+%283x%2B7%29 equal to 1