SOLUTION: Find the exact length of the side of a square whose digonal is 3 feet.

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Question 174216: Find the exact length of the side of a square whose digonal is 3 feet.
Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
pathagorean theorem states a%5E2%2Bb%5E2=c%5E2where a and b are legs and c is the hypothenuse. In our case of a square both legs (lets call them a) are equal and the hypothenuse is 3
:
a%5E2%2Ba%5E2=3%5E2
:
2a%5E2-9=0
:
a%5E2=9%2F2 a=sqrt%289%2F2%29 a=sqrt%2818%29%2F2 a=3sqrt%282%29%2F2
:
so our sides are 3sqrt%282%29%2F2feet each
:
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B0x%2B-9+=+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=%280%29%5E2-4%2A2%2A-9=72.

Discriminant d=72 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+72+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+72+%29%29%2F2%5C2+=+2.12132034355964
x%5B2%5D+=+%28-%280%29-sqrt%28+72+%29%29%2F2%5C2+=+-2.12132034355964

Quadratic expression 2x%5E2%2B0x%2B-9 can be factored:
2x%5E2%2B0x%2B-9+=+%28x-2.12132034355964%29%2A%28x--2.12132034355964%29
Again, the answer is: 2.12132034355964, -2.12132034355964. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B0%2Ax%2B-9+%29