SOLUTION: Solve the equations. check the solutions. sqrt 2y+7+4=y

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Question 100516: Solve the equations. check the solutions.
sqrt 2y+7+4=y
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt 2y+7+4=y
sqrt(2y)=y-11 subtract ll from each side.
2y=y^2-22y+121 square each side
y^2-24y+121=0 subtract 2y from each side.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-24x%2B121+=+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=%28-24%29%5E2-4%2A1%2A121=92.

Discriminant d=92 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--24%2B-sqrt%28+92+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+92+%29%29%2F2%5C1+=+16.7958315233127
x%5B2%5D+=+%28-%28-24%29-sqrt%28+92+%29%29%2F2%5C1+=+7.20416847668728

Quadratic expression 1x%5E2%2B-24x%2B121 can be factored:
1x%5E2%2B-24x%2B121+=+%28x-16.7958315233127%29%2A%28x-7.20416847668728%29
Again, the answer is: 16.7958315233127, 7.20416847668728. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-24%2Ax%2B121+%29

graph%28500%2C500%2C-1%2C20%2C-30%2C10%2Cx%5E2-24x%2B121%29