SOLUTION: (sqrt(3)-2)*(5*sqrt(5)-x)=3*sqrt(3)-6

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Question 1000699: (sqrt(3)-2)*(5*sqrt(5)-x)=3*sqrt(3)-6
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
(sqrt(3)-2)*(5*sqrt(5)-x)=3*sqrt(3)-6
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(5*sqrt(5)-x)=3*(sqrt(3)-2)/(sqrt(3)-2)
(5*sqrt(5)-x) = 3
x%5E2+-+x%2A10sqrt%285%29+%2B+125+=+9
x%5E2+-+x%2Asqrt%28500%29+%2B+116+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B22.3606797749979x%2B116+=+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=%2822.3606797749979%29%5E2-4%2A1%2A116=36.0000000000002.

Discriminant d=36.0000000000002 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-22.3606797749979%2B-sqrt%28+36.0000000000002+%29%29%2F2%5Ca.




Quadratic expression 1x%5E2%2B22.3606797749979x%2B116 can be factored:
1x%5E2%2B22.3606797749979x%2B116+=+%28x--8.18033988749894%29%2A%28x--14.180339887499%29
Again, the answer is: -8.18033988749894, -14.180339887499. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B22.3606797749979%2Ax%2B116+%29

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The solver rounds off.
x+=+-5sqrt%285%29%2B3
x+=+-5sqrt%285%29-3

Answer by MathTherapy(10556) About Me  (Show Source):
You can put this solution on YOUR website!
(sqrt(3)-2)*(5*sqrt(5)-x)=3*sqrt(3)-6