SOLUTION: I'm not sure if I am solving this question on systems of equations right. the answer needs to be in simplest a+bi form: {{{y=2x^2-6x+7}}} y=x-4 my work: {{{x-4=2x^2-6x+7}

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Question 697070: I'm not sure if I am solving this question on systems of equations right. the answer needs to be in simplest a+bi form:
y=2x%5E2-6x%2B7
y=x-4
my work:
x-4=2x%5E2-6x%2B7
0=2x%5E2-7x%2B11
then I did the quadratic equation: negative B plus or minus sqrt%28b%5E2-4ac%29 divided by 2a
a=2
b=-7
c=11
4ac=22
7 plus or minus sqrt%2849-22%29 divided by 4= 7 plus or minus sqrt%2827%29 divided by 4.
Then you break sqrt%2827%29 down to sqrt%289%29 and sqrt%283%29 and get 3 sqrt%283%29.
My final answer was (7 plus or minus 3sqrt%283%29) divided by 4.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
I'm not sure if I am solving this question on systems of equations right. the answer needs to be in simplest a+bi form:
y=2x%5E2-6x%2B7
y=x-4
my work:
x-4=2x%5E2-6x%2B7
0=2x%5E2-7x%2B11
then I did the quadratic equation: negative B plus or minus sqrt%28b%5E2-4ac%29 divided by 2a
a=2
b=-7
c=11
4ac=22 ************* 4ac = 88
---------
You did it right, except for that.
Go from there.
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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 2x%5E2%2B-7x%2B11+=+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=%28-7%29%5E2-4%2A2%2A11=-39.

The discriminant -39 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 -39 is + or - sqrt%28+39%29+=+6.2449979983984.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-7%2Ax%2B11+%29