SOLUTION: 7X(1-X)= 5(X-2)

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Question 35941: 7X(1-X)= 5(X-2)
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
7X%281-X%29=+5%28X-2%29

7x+-7x%5E2+=+5x-+10

This is a quadratic equation because of the x%5E2 term, so the first step must be to set it equal to zero. To avoid a troublesome negative coefficient of x%5E2, I would move everything to the right side by adding %2B7x%5E2+-+7x to each side:
7x+-+7x%5E2+-+7x+%2B+7x%5E2+=+5x+-+10+-+7x+%2B+7x%5E2
0+=+7x%5E2+-+2x+-+10+

Hopefully this will factor: 0=+%287x_____%29%28x_____%29+

However, it does NOT. So let's invoke a quadratic equation solver from algebra.com.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 7x%5E2%2B-2x%2B-10+=+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=%28-2%29%5E2-4%2A7%2A-10=284.

Discriminant d=284 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+284+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+284+%29%29%2F2%5C7+=+1.34659282473948
x%5B2%5D+=+%28-%28-2%29-sqrt%28+284+%29%29%2F2%5C7+=+-1.06087853902519

Quadratic expression 7x%5E2%2B-2x%2B-10 can be factored:
7x%5E2%2B-2x%2B-10+=+%28x-1.34659282473948%29%2A%28x--1.06087853902519%29
Again, the answer is: 1.34659282473948, -1.06087853902519. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+7%2Ax%5E2%2B-2%2Ax%2B-10+%29



I think the answer you should get from this is reduces to +%281+%2B-+sqrt%2871%29%29%2F7.

R^2 at SCC