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