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Find the number that we can place in the box so that the resulting quadratic is the square of a binomial. \[x^2 + \dfrac{4}{5}x + \boxed{\phantom{000}}\]

 

I've seen similar problems, but I don't know how to solve them! Help please!

 Apr 13, 2020
 #1
avatar+23689 
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I think your question is

x2 + 4/5 x + ?         We need to 'complete the square'      take 1/2 of the x coefficient  (2/5) , square it , and add it to the equation

(x2 + 4/5 x   + 4/25)     then it becomes

 

(x+2/5)^2

 Apr 13, 2020
 #2
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thank you!

SavvyBee  Apr 14, 2020

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