Find the Perfect Square Trinomial x^2+12/7x

$x^{2} + \frac{12}{7} x$

Step 1

Combine $\frac{12}{7}$ and $x$ .

$x^{2} + \frac{12 x}{7}$

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.

${(\frac{12}{7} \cdot \frac{1}{2})}^{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

${(\frac{2 (6)}{7} \cdot \frac{1}{2})}^{2}$

Cancel the common factor.

${(\frac{2 \cdot 6}{7} \cdot \frac{1}{2})}^{2}$

Rewrite the expression.

${(\frac{6}{7})}^{2}$

Simplify the expression.

Apply the product rule to $\frac{6}{7}$ .

$\frac{6^{2}}{7^{2}}$

Raise $6$ to the power of $2$ .

$\frac{36}{7^{2}}$

Raise $7$ to the power of $2$ .

$\frac{36}{49}$

Step 3

Add $\frac{36}{49}$ to get the perfect square trinomial.

$x^{2} + \frac{12}{7} x + \frac{36}{49}$