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

$2 x^{2} + 7 x$

Factor out the $2$

$2 (x^{2} + \frac{7 x}{2})$

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.

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

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

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

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

Multiply $2$ by $2$ .

${(\frac{7}{4})}^{2}$

Apply the product rule to $\frac{7}{4}$ .

$\frac{7^{2}}{4^{2}}$

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

$\frac{49}{4^{2}}$

Raise $4$ to the power of $2$ .

$\frac{49}{16}$

Add $\frac{49}{16}$ to get the perfect square trinomial.

$2 (x^{2} + \frac{7 x}{2} + \frac{49}{16})$

Simplify.

Apply the distributive property.

$2 x^{2} + 2 \frac{7 x}{2} + 2 (\frac{49}{16})$

Simplify.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x^{2} + 2 \frac{7 x}{2} + 2 (\frac{49}{16})$

Rewrite the expression.

$2 x^{2} + 7 x + 2 (\frac{49}{16})$

Cancel the common factor of $2$ .

Factor $2$ out of $16$ .

$2 x^{2} + 7 x + 2 \frac{49}{2 (8)}$

Cancel the common factor.

$2 x^{2} + 7 x + 2 \frac{49}{2 \cdot 8}$

Rewrite the expression.

$2 x^{2} + 7 x + \frac{49}{8}$