Find the Perfect Square Trinomial x^2+x+1

$x^{2} + x + 1$

Step 1

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $x$ by $2$ and square the result.

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{2}}{2^{2}}$

One to any power is one.

$\frac{1}{2^{2}}$

Raise $2$ to the power of $2$ .

$\frac{1}{4}$

Step 2

Add $\frac{1}{4}$ to get the perfect square trinomial.

Write $1$ as a fraction with a common denominator.

$x^{2} + x + \frac{4}{4} + \frac{1}{4}$

Combine the numerators over the common denominator.

$x^{2} + x + \frac{4 + 1}{4}$

Add $4$ and $1$ .

$x^{2} + x + \frac{5}{4}$