Algebra Examples

4 x^{2} - 5 x

$4 x^{2} - 5 x$

Step 1

Factor out the

4

$4$

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

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

Step 2

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 2.1

Multiply the numerator by the reciprocal of the denominator.

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

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

Step 2.2

Multiply

\frac{5}{4} \cdot \frac{1}{2}

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

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Step 2.2.1

Multiply

\frac{5}{4}

$\frac{5}{4}$ by

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 2.2.2

Multiply

4

$4$ by

2

$2$ .

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

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

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

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

Step 2.3

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 2.3.1

Apply the product rule to

- \frac{5}{8}

$- \frac{5}{8}$ .

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

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

Step 2.3.2

Apply the product rule to

\frac{5}{8}

$\frac{5}{8}$ .

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

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

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

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

Step 2.4

Raise

- 1

$- 1$ to the power of

2

$2$ .

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

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

Step 2.5

Multiply

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

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

1

$1$ .

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

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

Step 2.6

Raise

5

$5$ to the power of

2

$2$ .

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

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

Step 2.7

Raise

8

$8$ to the power of

2

$2$ .

\frac{25}{64}

$\frac{25}{64}$

\frac{25}{64}

$\frac{25}{64}$

Step 3

Add

\frac{25}{64}

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

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

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

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})

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

Step 4.2

Simplify.

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Step 4.2.1

Cancel the common factor of

4

$4$ .

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Step 4.2.1.1

Move the leading negative in

- \frac{5 x}{4}

$- \frac{5 x}{4}$ into the numerator.

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

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

Step 4.2.1.2

Cancel the common factor.

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

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

Step 4.2.1.3

Rewrite the expression.

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

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

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

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

Step 4.2.2

Cancel the common factor of

4

$4$ .

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Step 4.2.2.1

Factor

4

$4$ out of

64

$64$ .

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

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

Step 4.2.2.2

Cancel the common factor.

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

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

Step 4.2.2.3

Rewrite the expression.

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

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

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

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

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

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

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

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

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