SOLUTION: 3x^2+12x+5=p(x+q)^2+r Find the values of p,q and r

Question 363908: 3x^2+12x+5=p(x+q)^2+r
Find the values of p,q and r
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

FOIL

Distribute.

Notice that the coefficients for the terms are (on the left) and (on the right). So

So the equation becomes

Multiply

Now notice that the coefficients for the x terms are 12 and 6q. So , which means that

So the equation then becomes and simplifies to

Finally, we see that 12+r=5, which means that

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