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Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial.

x^2 + 8x + ____ + 3x^2 + 2x

 Aug 1, 2021
 #1
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x^2 + 8x + ____ + 3x^2 + 2x      condense

4x^2 + 10x + _____   

4 (x^2 + 2.5x) + ____

4 (x + 1.25)^2

4x^2 +10x  + 25/4            =  (2x +2.5)^2

 Aug 1, 2021
edited by ElectricPavlov  Aug 1, 2021
 #2
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Let's simplify first: 4x^2 + 10x + ____ is the square of a binomial

(a + b)^2 = a^2 + b^2 + 2ab

so (2x + 2.5)^2, so that means ____ = 25/4. 

Guest Aug 1, 2021

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