SOLUTION: Solve the equation. Square root sign x +43= x+1 The solution set is { }

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Question 892955: Solve the equation.
Square root sign x +43= x+1
The solution set is { }
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Use sqrt for sq roots.
sqrt(x) + 43 = x+1
sqrt(x) = x - 42
Square both sides
x = x^2 - 84x + 1764
x^2 - 85x + 1764 = 0
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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 1x%5E2%2B-85x%2B1764+=+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=%28-85%29%5E2-4%2A1%2A1764=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--85%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-85%29%2Bsqrt%28+169+%29%29%2F2%5C1+=+49
x%5B2%5D+=+%28-%28-85%29-sqrt%28+169+%29%29%2F2%5C1+=+36

Quadratic expression 1x%5E2%2B-85x%2B1764 can be factored:
1x%5E2%2B-85x%2B1764+=+%28x-49%29%2A%28x-36%29
Again, the answer is: 49, 36. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-85%2Ax%2B1764+%29