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Fill in the blank, so that that the resulting expression is the square of a binomial:

 

x^2 + 6/5*x + ___

 Oct 11, 2020
 #1
avatar+10324 
+1

Fill in the blank, so that that the resulting expression is the square of a binomial:
x^2 + 6/5*x +__

 

Hello Guest!

 

\(x^2+\frac{6}{5}x+\)__

 

\(a^2+2ab+b^2\\ a=x\\ 2ab=\frac{5}{6}x\)

\(2xb=\frac{6}{5}x\\ b=\frac{6\cdot x}{5\cdot 2\cdot x}\\ b=\frac{3}{5}\)

\(x^2+\frac{6}{5}x+(\frac{3}{5})^2=(x+\frac{3}{5})^2\)

laugh  !

 Oct 11, 2020
 #2
avatar+27695 
+1

Take 1/2  of the 'x' coefficient , square it and add it to the expression to 'complete the square

[(1/2)(6/5) ]2 =   36/100      or   9/25     for the blank

 Oct 11, 2020

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