Precalculus Examples

x^{2} - 19 x

$x^{2} - 19 x$

Step 1

To find the

c

$c$ value

c = {(\frac{b}{2})}^{2}

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

x

$x$ by

2

$2$ and square the result.

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Step 1.1

Use the power rule

{(a b)}^{n} = a^{n} b^{n}

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

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Step 1.1.1

Apply the product rule to

- \frac{19}{2}

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

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

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

Step 1.1.2

Apply the product rule to

\frac{19}{2}

$\frac{19}{2}$ .

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

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

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

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

Step 1.2

Raise

- 1

$- 1$ to the power of

2

$2$ .

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

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

Step 1.3

Multiply

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

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

1

$1$ .

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

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

Step 1.4

Raise

19

$19$ to the power of

2

$2$ .

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

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

Step 1.5

Raise

2

$2$ to the power of

2

$2$ .

\frac{361}{4}

$\frac{361}{4}$

\frac{361}{4}

$\frac{361}{4}$

Step 2

Add

\frac{361}{4}

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

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

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

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