SOLUTION: How would you solve problems like: x^2+5=0 x^2-11=0 Why is there two solutions? Thank you

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Question 194972: How would you solve problems like:
x^2+5=0
x^2-11=0
Why is there two solutions?
Thank you
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How would you solve problems like:
x^2+5=0
x^2-11=0
Why is there two solutions?
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x^2+5=0
Since there's no x term:
x%5E2+=+-5
x = ± i*sqrt(5) where i = sqrt(-1)
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x^2-11=0
x%5E2+=+11
x = +sqrt(11)
x = -sqrt(11)
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There are 2 solutions because both work.
In the 2nd eqn, both +sqrt(11) and -sqrt(11) are 11 when they're multiplied by themselves.
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-11+=+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=%280%29%5E2-4%2A1%2A-11=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+44+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+3.3166247903554
x%5B2%5D+=+%28-%280%29-sqrt%28+44+%29%29%2F2%5C1+=+-3.3166247903554

Quadratic expression 1x%5E2%2B0x%2B-11 can be factored:
1x%5E2%2B0x%2B-11+=+%28x-3.3166247903554%29%2A%28x--3.3166247903554%29
Again, the answer is: 3.3166247903554, -3.3166247903554. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-11+%29

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If you graph them, you'll see that they cross the x-axis in 2 places (the 2nd one).
You can get FREE software to graph these at
www.padowan.dk.com/graph/