Examples

$4 x^{2} - 5 x$

Step 1

Factor out the $4$

$4 (x^{2} - \frac{5 x}{4})$

Step 2

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 2.1

Multiply the numerator by the reciprocal of the denominator.

${(- (\frac{5}{4} \cdot \frac{1}{2}))}^{2}$

Step 2.2

Multiply $\frac{5}{4} \cdot \frac{1}{2}$ .

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Step 2.2.1

Multiply $\frac{5}{4}$ by $\frac{1}{2}$ .

${(- \frac{5}{4 \cdot 2})}^{2}$

Step 2.2.2

Multiply $4$ by $2$ .

${(- \frac{5}{8})}^{2}$

Step 2.3

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

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Step 2.3.1

Apply the product rule to $- \frac{5}{8}$ .

${(- 1)}^{2} {(\frac{5}{8})}^{2}$

Step 2.3.2

Apply the product rule to $\frac{5}{8}$ .

${(- 1)}^{2} \frac{5^{2}}{8^{2}}$

Step 2.4

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

$1 \frac{5^{2}}{8^{2}}$

Step 2.5

Multiply $\frac{5^{2}}{8^{2}}$ by $1$ .

$\frac{5^{2}}{8^{2}}$

Step 2.6

Raise $5$ to the power of $2$ .

$\frac{25}{8^{2}}$

Step 2.7

Raise $8$ to the power of $2$ .

$\frac{25}{64}$

Step 3

Add $\frac{25}{64}$ to get the perfect square trinomial.

$4 (x^{2} - \frac{5 x}{4} + \frac{25}{64})$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$4 x^{2} + 4 (- \frac{5 x}{4}) + 4 (\frac{25}{64})$

Step 4.2

Simplify.

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Step 4.2.1

Cancel the common factor of $4$ .

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Step 4.2.1.1

Move the leading negative in $- \frac{5 x}{4}$ into the numerator.

$4 x^{2} + 4 \frac{- 5 x}{4} + 4 (\frac{25}{64})$

Step 4.2.1.2

Cancel the common factor.

$4 x^{2} + 4 \frac{- 5 x}{4} + 4 (\frac{25}{64})$

Step 4.2.1.3

Rewrite the expression.

$4 x^{2} - 5 x + 4 (\frac{25}{64})$

Step 4.2.2

Cancel the common factor of $4$ .

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Step 4.2.2.1

Factor $4$ out of $64$ .

$4 x^{2} - 5 x + 4 \frac{25}{4 (16)}$

Step 4.2.2.2

Cancel the common factor.

$4 x^{2} - 5 x + 4 \frac{25}{4 \cdot 16}$

Step 4.2.2.3

Rewrite the expression.

$4 x^{2} - 5 x + \frac{25}{16}$

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