Thursday, April 3, 2014

Solve this equation: d^2-5d+6=0

d%5E2-5d%2B6=0

then...we'll use grouping to solve.

After looking at the factors 6 and 1 we notice that they don't quite work, so let's try 3 and 3:
d%5E2-5d%2B6=d%5E2-2d-3d%2B6=%28d%5E2-2d%29-%283d-6%29

Next we factor out the greatest common factors then we group them:
%28d%5E2-2d%29-%283d-6%29=d%28d-2%29-3%28d-2%29=%28d-3%29%28d-2%29

so that

%28d-3%29%28d-2%29=0

Finally, because of the zero product property we can see that
x=3 or x=2 

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