SOLUTION: Y+11=2X 2X TO THE SECOND +Y TO THE SECOND = 41

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Question 437133: Y+11=2X
2X TO THE SECOND +Y TO THE SECOND = 41
Answer by oberobic(2304) About Me  (Show Source):
You can put this solution on YOUR website!
We're told:
y+11=2x
Subtracting 11 from both sides:
y = 2x -11
.
We're told:
x^2 + y^2 = 41
.
Substitute y = 2x-11:
x^2 + (2x-11)^2 = 41
x^2 + 4x^2 -44x + 121 = 41
5x^2 -44x +80 = 0
.
This will not factor easily, so you can use the quadratic equation;
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-44x%2B80+=+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=%28-44%29%5E2-4%2A5%2A80=336.

Discriminant d=336 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--44%2B-sqrt%28+336+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-44%29%2Bsqrt%28+336+%29%29%2F2%5C5+=+6.23303027798234
x%5B2%5D+=+%28-%28-44%29-sqrt%28+336+%29%29%2F2%5C5+=+2.56696972201766

Quadratic expression 5x%5E2%2B-44x%2B80 can be factored:
5x%5E2%2B-44x%2B80+=+5%28x-6.23303027798234%29%2A%28x-2.56696972201766%29
Again, the answer is: 6.23303027798234, 2.56696972201766. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-44%2Ax%2B80+%29