SOLUTION: the sum of the square of two number is 39, the first number being one less their twice the second number. determine the numbers.

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Question 909856: the sum of the square of two number is 39, the first number being one less their twice the second number. determine the numbers.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
(2x-1)^2 + x^2 = 39
4x^2 - 4x + 1 + x^2 = 39
5x^2 - 4x - 38 = 0
x = 3.18567765543682, -2.38567765543682
find corresponding values for (2x-1)to determine the number pairs.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-4x%2B-38+=+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=%28-4%29%5E2-4%2A5%2A-38=776.

Discriminant d=776 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+776+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+776+%29%29%2F2%5C5+=+3.18567765543682
x%5B2%5D+=+%28-%28-4%29-sqrt%28+776+%29%29%2F2%5C5+=+-2.38567765543682

Quadratic expression 5x%5E2%2B-4x%2B-38 can be factored:
5x%5E2%2B-4x%2B-38+=+5%28x-3.18567765543682%29%2A%28x--2.38567765543682%29
Again, the answer is: 3.18567765543682, -2.38567765543682. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-4%2Ax%2B-38+%29