SOLUTION: how can i get the value/s of x in the equation: (square root of x) - 3 = x-15?

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Question 220643: how can i get the value/s of x in the equation: (square root of x) - 3 = x-15?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28x%29+-+3+=+x-15
sqrt%28x%29+=+x-18
Square both sides:
x+=+%28x-18%29%28x-18%29
x+=+x%5E2-36x-324%29
0+=+x%5E2-35x-324%29
Can't factor so use the "quadratic equation". Doing so yields:
x = {42.60, -7.60}
.
Details of the quadratic equation follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-35x%2B-324+=+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=%28-35%29%5E2-4%2A1%2A-324=2521.

Discriminant d=2521 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--35%2B-sqrt%28+2521+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-35%29%2Bsqrt%28+2521+%29%29%2F2%5C1+=+42.6047804212664
x%5B2%5D+=+%28-%28-35%29-sqrt%28+2521+%29%29%2F2%5C1+=+-7.60478042126638

Quadratic expression 1x%5E2%2B-35x%2B-324 can be factored:
1x%5E2%2B-35x%2B-324+=+1%28x-42.6047804212664%29%2A%28x--7.60478042126638%29
Again, the answer is: 42.6047804212664, -7.60478042126638. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-35%2Ax%2B-324+%29