Find the Perfect Square Trinomial x^2-1/7x

$x^{2} - \frac{1}{7} x$

Step 1

Combine $x$ and $\frac{1}{7}$ .

$x^{2} - \frac{x}{7}$

Step 2

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

Multiply the numerator by the reciprocal of the denominator.

${(- \frac{1}{7} \cdot \frac{1}{2})}^{2}$

Multiply $- \frac{1}{7} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{1}{7}$ .

${(- \frac{1}{2 \cdot 7})}^{2}$

Multiply $2$ by $7$ .

${(- \frac{1}{14})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{1}{14}$ .

${(- 1)}^{2} {(\frac{1}{14})}^{2}$

Apply the product rule to $\frac{1}{14}$ .

${(- 1)}^{2} \frac{1^{2}}{14^{2}}$

Raise $- 1$ to the power of $2$ .

$1 \frac{1^{2}}{14^{2}}$

Multiply $\frac{1^{2}}{14^{2}}$ by $1$ .

$\frac{1^{2}}{14^{2}}$

One to any power is one.

$\frac{1}{14^{2}}$

Raise $14$ to the power of $2$ .

$\frac{1}{196}$

Step 3

Add $\frac{1}{196}$ to get the perfect square trinomial.

$x^{2} - \frac{1}{7} x + \frac{1}{196}$