Algebra Examples

$4 x^{2} + 12 x + c$

Step 1

Move $12 x$ .

$4 x^{2} + c + 12 x$

Step 2

Factor out the $4$

$4 (x^{2} + 3 x + \frac{c}{4})$

Step 3

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 3.1

Apply the product rule to $\frac{3}{2}$ .

$\frac{3^{2}}{2^{2}}$

Step 3.2

Raise $3$ to the power of $2$ .

$\frac{9}{2^{2}}$

Step 3.3

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

$\frac{9}{4}$

Step 4

Add $\frac{9}{4}$ to get the perfect square trinomial.

$4 (x^{2} + 3 x + \frac{c}{4} + \frac{9}{4})$

Step 5

Simplify.

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Step 5.1

Apply the distributive property.

$4 x^{2} + 4 (3 x) + 4 \frac{c}{4} + 4 (\frac{9}{4})$

Step 5.2

Simplify.

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Step 5.2.1

Multiply $3$ by $4$ .

$4 x^{2} + 12 x + 4 \frac{c}{4} + 4 (\frac{9}{4})$

Step 5.2.2

Cancel the common factor of $4$ .

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Step 5.2.2.1

Cancel the common factor.

$4 x^{2} + 12 x + 4 \frac{c}{4} + 4 (\frac{9}{4})$

Step 5.2.2.2

Rewrite the expression.

$4 x^{2} + 12 x + c + 4 (\frac{9}{4})$

Step 5.2.3

Cancel the common factor of $4$ .

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Step 5.2.3.1

Cancel the common factor.

$4 x^{2} + 12 x + c + 4 (\frac{9}{4})$

Step 5.2.3.2

Rewrite the expression.

$4 x^{2} + 12 x + c + 9$