SOLUTION: Please help me solve this equation: sqrt(2x+11)-sqrt(x+9)=sqrt(x-6)

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Question 1050203: Please help me solve this equation:
sqrt(2x+11)-sqrt(x+9)=sqrt(x-6)
Found 2 solutions by advanced_Learner, ikleyn:
Answer by advanced_Learner(501) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%282x%2B11%29-sqrt%28x%2B9%29=sqrt%28x-6%29


%282x%2B11%29-2*sqrt%282x%2B11%29*sqrt%28x%2B9%29+%28x%2B9%29=%28x-6%29

%283x%2B20%29-2*sqrt%282x%2B11%29*sqrt%28x%2B9%29=%28x-6%29

%283x%2B20%29-%28x-6%29=2*sqrt%282x%2B11%29*sqrt%28x%2B9%29
%282x%2B26%29=2*sqrt%282x%2B11%29*sqrt%28x%2B9%29
%284x%5E2%2B104x%2B676%29=4*%282x%2B11%29*%28x%2B9%29
%284x%5E2%2B104x%2B676%29=4*%282x%5E2%2B18x%2B11x%2B99%29
%284x%5E2%2B104x%2B676%29=%288x%5E2%2B72x%2B44x%2B396%29
simplify
%280%29=%284x%5E2%2B12x-280%29
thanks to quadratic solver
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B12x%2B-280+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A4%2A-280=4624.

Discriminant d=4624 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+4624+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+4624+%29%29%2F2%5C4+=+7
x%5B2%5D+=+%28-%2812%29-sqrt%28+4624+%29%29%2F2%5C4+=+-10

Quadratic expression 4x%5E2%2B12x%2B-280 can be factored:
4x%5E2%2B12x%2B-280+=+4%28x-7%29%2A%28x--10%29
Again, the answer is: 7, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B12%2Ax%2B-280+%29

Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
Of the two roots x = 7 and x = -10, only the root x = 7 satisfies the original equation.

The other root, x = -10, is extraneous and does not satisfies the original equation.



Plots y = sqrt%282x%2B11%29-sqrt%28x%2B9%29 (red) and y = sqrt%28x-6%29 (green)