Answer:
Last option: 4
Step-by-step explanation:
The quadratic equation simplified: [tex]x^2-4x=-\frac{7}{2}[/tex] has the form:
[tex]ax^2+bx=c[/tex]
In this case, you can identify that "a", "b" and "c" are:
[tex]a=1\\b=-4\\c=-\frac{7}{2}[/tex]
To solve this quadratic equation by completing the square, Carlos should add [tex](\frac{b}{2})^2[/tex] to both sides of the equation. This is:
[tex](\frac{-4}{2})^2=(-2)^2=4[/tex]
Then:
[tex]x^2-4x+4=-\frac{7}{2}+4[/tex]
Therefore you can observe that the number he should add to both sides of the equation is: 4
