SOLUTION: Radical x+10 (end radical)= x-2

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Question 667475: Radical x+10 (end radical)= x-2
Answer by jerryguo41(197) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%2B10%29=x-2
x%2B10=%28x-2%29%5E2
x%2B10=x%5E2-4x%2B4
0=x%5E2-5x-6
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B-6+=+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=%28-5%29%5E2-4%2A1%2A-6=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+49+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-5%29-sqrt%28+49+%29%29%2F2%5C1+=+-1

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