The number 16 must be added to the equation for making it a perfect square.
We must have the idea of algebraic identities to solve this problem. The identity of the sum of square of two variables is given below.
We know that [tex](a+b)^{2}= a^{2} +2ab+b^{2}[/tex].
So make a perfect square the equation must be of the form of [tex]a^{2} +2ab+b^{2}[/tex]
Given, [tex]x^{2} +8x=4[/tex]
⇒ [tex]x^{2} +2*4*x+ 4^{2}=4+4^{2}[/tex]
⇒ [tex](x+4)^{2}=20[/tex]
So, to complete the square we have added 16 to both the sides of the equation and now it is in the form of [tex](a+b)^{2}[/tex].
The required number to be added is 16.
To learn more about the algebraic identities visit the link:
https://brainly.com/question/16857438
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