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)   (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 (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

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 - .

The solution is

Here's your graph:
Answer by bucky(2189)   (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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Subtract 2x from both sides to get:
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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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Add the two terms on the right side to get:
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Factor the left side (a perfect square that we made) to make the equation become:
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Take the square root of both sides:
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Add +1 to both sides:
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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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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.

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