Question 221447: Solve for x. x^2+45=6x
Thank you!
Found 2 solutions by checkley77, likaaka:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! Solve for x. x^2+45=6x
x^2-6x+45=0
x=(6+-sqrt[-6^2-4*1*45])/2*1
x=(6+-sqrt[36-180)/2
x=(6+-sqrt-144)/2
x=(6+-12i)/2
x=6/2+-12i/2
x=3+-6i ans.
Answer by likaaka(51) (Show Source):
You can put this solution on YOUR website! First we set the equation to 0
x^2 + 45 = 6x subtract 6x from both sides
x^2 - 6x + 45 = 0
Now you must use the quadratic equation to solve
where ax^2 + bx + c = 0, and a can not equal 0
| 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 -144 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 -144 is + or -  .
The solution is 
Here's your graph:
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Basically when you work out the quadratic equation, you end up with a negative number under the radical which gives you an imaginary number. Unless you have been working with imaginary numbers, this means there is no solution. Graphically, when you solve for x, you are trying to find the x-intercepts. In this case, the graph never crosses the x-axis and there are no x-intercepts.
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