SOLUTION: {{{ 5 sqrt (x) - x = 6 }}}

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Question 986091: +5+sqrt+%28x%29+-+x+=+6+
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
+5sqrt%28x%29+-+x+=+6+
+5sqrt%28x%29+=+x+%2B+6+
Square both sided
25x+=+x%5E2+%2B+12x+%2B+36
x%5E2+-13x+%2B+36+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-13x%2B36+=+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=%28-13%29%5E2-4%2A1%2A36=25.

Discriminant d=25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--13%2B-sqrt%28+25+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-13%29%2Bsqrt%28+25+%29%29%2F2%5C1+=+9
x%5B2%5D+=+%28-%28-13%29-sqrt%28+25+%29%29%2F2%5C1+=+4

Quadratic expression 1x%5E2%2B-13x%2B36 can be factored:
1x%5E2%2B-13x%2B36+=+1%28x-9%29%2A%28x-4%29
Again, the answer is: 9, 4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-13%2Ax%2B36+%29

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x = 4
x = 9