Examples

$x^{2} - 19 x$

Step 1

To find the

$c$ value

$c = {(\frac{b}{2})}^{2}$ , divide the coefficient of

$x$ by

$2$ and square the result.

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Step 1.1

Use the power rule

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

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Step 1.1.1

Apply the product rule to

$- \frac{19}{2}$ .

${(- 1)}^{2} {(\frac{19}{2})}^{2}$

Step 1.1.2

Apply the product rule to

$\frac{19}{2}$ .

${(- 1)}^{2} \frac{19^{2}}{2^{2}}$

Step 1.2

Raise

$- 1$ to the power of

$2$ .

$1 \frac{19^{2}}{2^{2}}$

Step 1.3

Multiply

$\frac{19^{2}}{2^{2}}$ by

$1$ .

$\frac{19^{2}}{2^{2}}$

Step 1.4

Raise

$19$ to the power of

$2$ .

$\frac{361}{2^{2}}$

Step 1.5

Raise

$2$ to the power of

$2$ .

$\frac{361}{4}$

Step 2

Add

$\frac{361}{4}$ to get the perfect square trinomial.

$x^{2} - 19 x + \frac{361}{4}$

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