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you have: Which value must be added to the expression \(x^{2} +x\)

to make it a perfect-square trinomial?

\(x^{2} +x+ \frac{1}{4}\) (Answer)

A perfect square is a whole number that is the square of an integer..-->>>

EX: 16 is a perfect square because 4*4=16

\(x^{2} +x+ \frac{1}{2}\)-->>(No)

This expression can't be factored with rational numbers, nor is the polynomial factorable with rational numbers.

\(x^{2} +x+1\)-->>(No)

This expression can't be factored with rational numbers, nor is the polynomial factorable with rational numbers.

\(x^{2} +x+4\)-->>(No)

This expression can't be factored with rational numbers, nor is the polynomial factorable with rational numbers.

Thus, your answer.

calculista

we know that

Perfect square trinomials are quadratics which are the results of squaring binomials

so

\(x^{2} +2ax+a^{2} =(x+a)^{2}\)

we have

\(x^{2} + x\)

Divide the coefficient of the term x by \(2\)

\(=\frac{1}{2}\)

\((x+\frac{1}{2} )^{2} = x^{2}+2x*\frac{1}{2} +\frac{1}{4} \\\\ (x+\frac{1}{2} )^{2} = x^{2}+x +\frac{1}{4}\)

therefore

the answer is the option

A. 1/4

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