SOLUTION: (radical sign)2x +11= x + 7

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Question 627353: (radical sign)2x +11= x + 7
Found 2 solutions by Bunni, jim_thompson5910:
Answer by Bunni(2) About Me  (Show Source):
You can put this solution on YOUR website!
not sure, but i believe the answer is... - 4 if you get it wrong then you can send me a hate mail or something ^.^

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B11%29+=+x%2B7

2x%2B11+=+%28x%2B7%29%5E2

2x%2B11+=+x%5E2%2B14x%2B49

0+=+x%5E2%2B14x%2B49-2x-11

0+=+x%5E2%2B12x%2B38

x%5E2%2B12x%2B38+=+0

Now let's use the quadratic formula for x

x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29

x+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%281%29%2838%29+%29%29%2F%282%281%29%29

x+=+%28-12+%2B-+sqrt%28+-8+%29%29%2F%282%29

Since you can't take the square root of a negative number, this means that there are no real solutions to sqrt%282x%2B11%29+=+x%2B7.
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sqrt%282x%29%2B11+=+x%2B7

sqrt%282x%29+=+x%2B7-11

sqrt%282x%29+=+x-4

2x+=+%28x-4%29%5E2

2x+=+x%5E2+-+8x+%2B+16

0+=+x%5E2+-+8x+%2B+16-2x

0+=+x%5E2+-+10x+%2B+16

x%5E2+-+10x+%2B+16+=+0

Now let's use the quadratic formula for x

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

x+=+%28-%28-10%29%2B-sqrt%28%28-10%29%5E2-4%281%29%2816%29%29%29%2F%282%281%29%29

x+=+%2810%2B-sqrt%28100-%2864%29%29%29%2F%282%29

x+=+%2810%2B-sqrt%2836%29%29%2F2

x+=+%2810%2Bsqrt%2836%29%29%2F2 or x+=+%2810-sqrt%2836%29%29%2F2

x+=+%2810%2B6%29%2F2 or x+=+%2810-6%29%2F2

x+=+16%2F2 or x+=+4%2F2

x+=+8 or x+=+2

So the possible solutions to sqrt%282x%29%2B11+=+x%2B7 are x+=+8 or x+=+2

Make sure you check them (I'll let you do this)