SOLUTION: What number is equal to three less than its square? Please help me and show me the solution if possible with detailed explanation. Thank you!

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Question 766863: What number is equal to three less than its square?
Please help me and show me the solution if possible with detailed explanation. Thank you!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What number is equal to three less than its square?
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x = x^2 - 3
x%5E2+-+x+-+3+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-3+=+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=%28-1%29%5E2-4%2A1%2A-3=13.

Discriminant d=13 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+13+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+13+%29%29%2F2%5C1+=+2.30277563773199
x%5B2%5D+=+%28-%28-1%29-sqrt%28+13+%29%29%2F2%5C1+=+-1.30277563773199

Quadratic expression 1x%5E2%2B-1x%2B-3 can be factored:
1x%5E2%2B-1x%2B-3+=+%28x-2.30277563773199%29%2A%28x--1.30277563773199%29
Again, the answer is: 2.30277563773199, -1.30277563773199. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-3+%29

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