For this case we have the following expression:
[tex]x^2 + x[/tex]
We want to find a constant to create a perfect-square trinomial
The value of the constant is given by:
[tex]k = (\frac {b} {2}) ^ 2[/tex]
Where, b belongs to the coefficient that accompanies the term of exponent 1 in the quadratic equation.
[tex]b = 1[/tex]
Substituting values:
[tex]k = (\frac {1} {2}) ^ 2\\k = \frac {1} {4}[/tex]
Rewriting the expression we have:
[tex]x^2 + x + \frac {1} {4} = (x + \frac {1} {2}) (x+\frac {1} {2})\\x^2 + x + \frac {1} {4} = (x + \frac {1} {2}) ^ 2[/tex]
Answer:
[tex]k = \frac {1} {4}[/tex] must be added to the expression [tex]x^2 + x[/tex] to make it a perfect-square trinomial
