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Question 188276: Find a value for k that will make 4x^2 + 6.4 x + k a perfect square. Describe the procedure that you used which requires algebra [that is, not trial and error].
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Find a value for k that will make 4x^2 + 6.4 x + k a perfect square. Describe the procedure that you used which requires algebra [that is, not trial and error].
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Make it easier by dividing by 4
x^2 + 1.6x + k/4 = (x + c)^2
x^2 + 1.6x + k/4 = x^2 + 2cx + c^2
The term k/4 is the coefficient of x, 1.6, divided by 2 and squared.
c = 1.6/2 = 0.8
k/4 = c^2 = 0.64
k = 2.56
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(2x + 1.6)^2 = 4x^2 + 6.4x + 2.56 looks good
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