Perfect Square: find k to make 4^2 + 6.4x + k perfect square

Find a value for k that will make 4^2 + 6.4x + k a perfect square. Describe the procedure that you use, which requires algebra (that is, not trial and error.)

I am stumped on this one.

Re: Perfect Square Help

Google "complete the square" or "completing the square".

Re: Perfect Square Help

denisep said:

Find a value for k that will make 4^2 + 6.4x + k a perfect square. Describe the procedure that you use, which requires algebra (that is, not trial and error.)

I am stumped on this one.

Click to expand...

I'm stumped too...do you perhaps mean this?

4x^2 + 6.4x + k

Please let us know the EXACT problem you're dealing with...then we can probably help you.

Re: Perfect Square Help

This is the exact equation given to find a perfect square.

4x^2 + 6.4x + k

Re: Perfect Square Help

ignore the k for a moment ...

4x[sup:2ysq85x9]2[/sup:2ysq85x9] + 6.4x

factor out the 4 ...

4(x[sup:2ysq85x9]2[/sup:2ysq85x9] + 1.6x)

divide the coefficient of the linear term (that's the 1.6) in half, square the result, and add to the expression in the parenthesis ...

4(x[sup:2ysq85x9]2[/sup:2ysq85x9] + 1.6x + .64)

distribute the 4 back ...

4x[sup:2ysq85x9]2[/sup:2ysq85x9] + 6.4x + 2.56

the quadratic expression above is a perfect square, and can be factored as (2x + 1.6)[sup:2ysq85x9]2[/sup:2ysq85x9]

so ... k = 2.56

go to the following site to learn more about completing the square ...

http://www.mathsisfun.com/algebra/completing-square.html