Option C: 16 is the number added to both sides of the equation to complete the square
Explanation:
The equation is [tex]x^{2}+8 x=4[/tex]
We need to determine the number that is added to both sides of the equation to complete the square.
We need to write the equation in the form of [tex]x^{2}+2 a x+a^{2}=(x+a)^{2}[/tex]
Solve for a:
[tex]2 a x=8 x[/tex]
Dividing by 2x, we have,
[tex]a=4[/tex]
Thus, the value of a is 4.
To write the equation in the form of [tex]x^{2}+2 a x+a^{2}=(x+a)^{2}[/tex]:
Adding [tex]4^2[/tex] to both sides of the equation, we have,
[tex]x^{2}+8 x+4^{2}=4+4^{2}[/tex]
[tex]x^{2}+8 x+16=4+16[/tex]
Complete the square,we get,
[tex](x+4)^{2}=20[/tex]
Hence, the number 16 is added to both sides of the equation to complete the square.
Thus, Option C is the correct answer.
