Precalculus Examples

2 x^{2} + 7 x

$2 x^{2} + 7 x$

Step 1

Factor out the

2

$2$

2 (x^{2} + \frac{7 x}{2})

$2 (x^{2} + \frac{7 x}{2})$

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{7}{2} \cdot \frac{1}{2})}^{2}

${(\frac{7}{2} \cdot \frac{1}{2})}^{2}$

Step 2.2

Multiply

\frac{7}{2} \cdot \frac{1}{2}

$\frac{7}{2} \cdot \frac{1}{2}$ .

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Step 2.2.1

Multiply

\frac{7}{2}

$\frac{7}{2}$ by

\frac{1}{2}

$\frac{1}{2}$ .

{(\frac{7}{2 \cdot 2})}^{2}

${(\frac{7}{2 \cdot 2})}^{2}$

Step 2.2.2

Multiply

2

$2$ by

2

$2$ .

{(\frac{7}{4})}^{2}

${(\frac{7}{4})}^{2}$

{(\frac{7}{4})}^{2}

${(\frac{7}{4})}^{2}$

Step 2.3

Apply the product rule to

\frac{7}{4}

$\frac{7}{4}$ .

\frac{7^{2}}{4^{2}}

$\frac{7^{2}}{4^{2}}$

Step 2.4

Raise

7

$7$ to the power of

2

$2$ .

\frac{49}{4^{2}}

$\frac{49}{4^{2}}$

Step 2.5

Raise

4

$4$ to the power of

2

$2$ .

\frac{49}{16}

$\frac{49}{16}$

\frac{49}{16}

$\frac{49}{16}$

Step 3

Add

\frac{49}{16}

$\frac{49}{16}$ to get the perfect square trinomial.

2 (x^{2} + \frac{7 x}{2} + \frac{49}{16})

$2 (x^{2} + \frac{7 x}{2} + \frac{49}{16})$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

2 x^{2} + 2 \frac{7 x}{2} + 2 (\frac{49}{16})

$2 x^{2} + 2 \frac{7 x}{2} + 2 (\frac{49}{16})$

Step 4.2

Simplify.

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Step 4.2.1

Cancel the common factor of

2

$2$ .

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Step 4.2.1.1

Cancel the common factor.

$2 x^{2} + 2 \frac{7 x}{2} + 2 (\frac{49}{16})$

Step 4.2.1.2

Rewrite the expression.

$2 x^{2} + 7 x + 2 (\frac{49}{16})$

Step 4.2.2

Cancel the common factor of

$2$ .

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Step 4.2.2.1

Factor

$2$ out of

$16$ .

$2 x^{2} + 7 x + 2 \frac{49}{2 (8)}$

Step 4.2.2.2

Cancel the common factor.

$2 x^{2} + 7 x + 2 \frac{49}{2 \cdot 8}$

Step 4.2.2.3

Rewrite the expression.

$2 x^{2} + 7 x + \frac{49}{8}$

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