SOLUTION: x^2=2x-26

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Question 503998: x^2=2x-26
Found 2 solutions by oberobic, bucky:
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 = 2x -26
x^2 -2x + 26 = 0
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Unfortunately, this is not easy to factor.
So, you use the quadratic equation.
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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-2x%2B26+=+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%2A1%2A26=-100.

The discriminant -100 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -100 is + or - sqrt%28+100%29+=+10.

The solution is x%5B12%5D+=+%28--2%2B-+i%2Asqrt%28+-100+%29%29%2F2%5C1+=++%28--2%2B-+i%2A10%29%2F2%5C1+

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B26+%29

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
We'll do this one by completing the square. You could just as well do it by using the quadratic formula.
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Given to solve:
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x%5E2+=+2x+-+26
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Subtract 2x from both sides to get:
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x%5E2+-+2x+=+-26
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Make the left side a perfect square by adding 1. However, when you do that you also have to add 1 to the right side as follows:
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x%5E2+-+2x+%2B+1+=+1+-26
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Add the two terms on the right side to get:
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x%5E2+-+2x+%2B+1+=+-25
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Factor the left side (a perfect square that we made) to make the equation become:
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%28x+-+1%29%5E2+=+-25
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Take the square root of both sides:
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x+-+1+=+sqrt%28-25%29
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Add +1 to both sides:
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x+=1+%2B-sqrt%28-25%29
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Note that the square root of a negative number is i times the square root of the positive value of the number. This makes the equation become:
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x+=+1+%2B-+%28sqrt%2825%29%29%2Ai
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+x+=+1+%2B-+5%2Ai
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And that's the answer you are looking for.
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Hope this review of both "completing the square" and complex numbers has been helpful to you.