SOLUTION: The diagonal of a squars is 2 m longer than a side. Find the length of a side?

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Question 295867: The diagonal of a squars is 2 m longer than a side. Find the length of a side?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
x=side
a^2+b^2=c^2
if a=x then b=x and c=x+2
x%5E2%2Bx%5E2=%28x%2B2%29%5E2
2x%5E2=%28x%2B2%29%28x%2B2%29
2x%5E2-%28x%5E2%2B4x%2B4%29=%28x%5E2%2B4x%2B4%29-%28x%5E2%2B4x%2B4%29
2x%5E2-x%5E2-4x-4=0
x%5E2-4x-4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-4x%2B-4+=+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%2A1%2A-4=32.

Discriminant d=32 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--4%2B-sqrt%28+32+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-4%29%2Bsqrt%28+32+%29%29%2F2%5C1+=+4.82842712474619
x%5B2%5D+=+%28-%28-4%29-sqrt%28+32+%29%29%2F2%5C1+=+-0.82842712474619

Quadratic expression 1x%5E2%2B-4x%2B-4 can be factored:
1x%5E2%2B-4x%2B-4+=+1%28x-4.82842712474619%29%2A%28x--0.82842712474619%29
Again, the answer is: 4.82842712474619, -0.82842712474619. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-4%2Ax%2B-4+%29