SOLUTION: This is the problem that I was given and th only way I know how to solve would be trial and error. Find a value for k that will make 4x^2 + 6.4x + k a perfect square. Describe t

Question 187570: This is the problem that I was given and th only way I know how to solve would be trial and error.
Find a value for k that will make 4x^2 + 6.4x + k a perfect square. Describe the procedure that you used which requires algebra [that is, not trial and error].
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find a value for k that will make 4x^2 + 6.4x + k a perfect square.
:
We want the coefficient of x^2 to be 1, divide by 4
x^2 + 1.6x + k/4
Take the coefficient of 1.6, divide it by 2: .8; then square it; k/4 = .64
giving us:
x^2 + 1.6x + .64
Multiply by 4; (k = 2.56)
4x^2 + 6.4x + 2.56
factors to:
(2x + 1.6)^2
:
k = 2.56
:
Check it; FOIL
(2x + 1.6)(2x + 1.6) = 4x^2 + 3.2x + 3.2x + 2.56 = 4x^2 + 6.4x + 2.56
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