SOLUTION: Solve. {{{ sqrt(x+6)+sqrt(2-x)=4 }}}

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Question 58843: Solve.
+sqrt%28x%2B6%29%2Bsqrt%282-x%29=4+
Answer by aaaaaaaa(138) About Me  (Show Source):
You can put this solution on YOUR website!
+sqrt%28x%2B6%29%2Bsqrt%282-x%29=4+
%28sqrt%28x%2B6%29%2Bsqrt%282-x%29%29%5E2=4%5E2
%28sqrt%28x%2B6%29%2Bsqrt%282-x%29%29%28sqrt%28x%2B6%29%2Bsqrt%282-x%29%29=16
%28x%2B6%29%2Bsqrt%28x%2B6%29sqrt%282-x%29%2Bsqrt%28x%2B6%29sqrt%282-x%29%2B%282-x%29=16
8%2B2sqrt%28x%2B6%29sqrt%282-x%29=16
-8=2sqrt%28x%2B6%29sqrt%282-x%29
-4=sqrt%28x%2B6%29sqrt%282-x%29
%28-4%29%5E2=%28sqrt%28x%2B6%29sqrt%282-x%29%29%5E2
16=%28x%2B6%29%282-x%29
16=2x-x%5E2%2B12-6x
0=-x%5E2-4x-4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B-4x%2B-4+=+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=%28-4%29%5E2-4%2A-1%2A-4=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-4%29%29%2F2%5C-1.
Expression can be factored: -1x%5E2%2B-4x%2B-4+=+-1%28x--2%29%2A%28x--2%29

Again, the answer is: -2, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B-4%2Ax%2B-4+%29



Let's check if the solution -2 works:
sqrt%28-2%2B6%29%2Bsqrt%282-%28-2%29%29+=+sqrt%284%29+%2B+sqrt%284%29+=+2%2B2+=+4
There you go!