Find the Perfect Square Trinomial x^2-9x+c

$x^{2} - 9 x + c$

Step 1

Move $- 9 x$ .

$x^{2} + c - 9 x$

Step 2

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

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

Apply the product rule to $- \frac{9}{2}$ .

${(- 1)}^{2} {(\frac{9}{2})}^{2}$

Apply the product rule to $\frac{9}{2}$ .

${(- 1)}^{2} \frac{9^{2}}{2^{2}}$

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

$1 \frac{9^{2}}{2^{2}}$

Multiply $\frac{9^{2}}{2^{2}}$ by $1$ .

$\frac{9^{2}}{2^{2}}$

Raise $9$ to the power of $2$ .

$\frac{81}{2^{2}}$

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

$\frac{81}{4}$