SOLUTION: X{X-5}=8+(X-3)

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Question 578740: X{X-5}=8+(X-3)
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
X{X-5}=8+(X-3)
x^2-5x=8+x-3
x^2-6x-5=0
x=3-sqrt(14), x=3+sqrt(14) (see below)
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B-5+=+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=%28-6%29%5E2-4%2A1%2A-5=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+56+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+56+%29%29%2F2%5C1+=+6.74165738677394
x%5B2%5D+=+%28-%28-6%29-sqrt%28+56+%29%29%2F2%5C1+=+-0.741657386773941

Quadratic expression 1x%5E2%2B-6x%2B-5 can be factored:
1x%5E2%2B-6x%2B-5+=+1%28x-6.74165738677394%29%2A%28x--0.741657386773941%29
Again, the answer is: 6.74165738677394, -0.741657386773941. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B-5+%29