Calculus Examples

$x^{2} - \frac{1}{2} x$

Step 1

Combine $x$ and $\frac{1}{2}$ .

$x^{2} - \frac{x}{2}$

Step 2

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

Tap for more steps...

Step 2.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

Multiply $2$ by $2$ .

${(- \frac{1}{4})}^{2}$

Step 2.3

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

Tap for more steps...

Step 2.3.1

Apply the product rule to $- \frac{1}{4}$ .

${(- 1)}^{2} {(\frac{1}{4})}^{2}$

Step 2.3.2

Apply the product rule to $\frac{1}{4}$ .

${(- 1)}^{2} \frac{1^{2}}{4^{2}}$

Step 2.4

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

$1 \frac{1^{2}}{4^{2}}$

Step 2.5

Multiply $\frac{1^{2}}{4^{2}}$ by $1$ .

$\frac{1^{2}}{4^{2}}$

Step 2.6

One to any power is one.

$\frac{1}{4^{2}}$

Step 2.7

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

$\frac{1}{16}$

Step 3

Add $\frac{1}{16}$ to get the perfect square trinomial.

$x^{2} - \frac{1}{2} x + \frac{1}{16}$