SOLUTION: _5___+__46____=2 2x+6 7x

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Question 75656: _5___+__46____=2
2x+6 7x
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
5%2F%282x%2B6%29%2B46%2F%287x%29=2
Multiply both sides by the LCD (which is 7x(2x+6)
5%2A7x%2B46%282x%2B6%29=14x%282x%2B6%29
35x%2B92x%2B276=28x%5E2%2B84x Distribute the 46 on the left and distribute the 7x on the right
127x%2B276=28x%5E2%2B84x Combine like terms
0=28x%5E2%2B84x-127x-276 Get all terms to one side
0=28x%5E2-43x-276 Combine like terms and simplify. Now use the quadratic formula to solve for x:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 28x%5E2%2B-43x%2B-276+=+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=%28-43%29%5E2-4%2A28%2A-276=32761.

Discriminant d=32761 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--43%2B-sqrt%28+32761+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-43%29%2Bsqrt%28+32761+%29%29%2F2%5C28+=+4
x%5B2%5D+=+%28-%28-43%29-sqrt%28+32761+%29%29%2F2%5C28+=+-2.46428571428571

Quadratic expression 28x%5E2%2B-43x%2B-276 can be factored:
28x%5E2%2B-43x%2B-276+=+28%28x-4%29%2A%28x--2.46428571428571%29
Again, the answer is: 4, -2.46428571428571. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+28%2Ax%5E2%2B-43%2Ax%2B-276+%29


So x=-2.4642857 and x=4