Algebra Examples

$x^{2} - 11 x$

Step 1

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 1.1

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

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Step 1.1.1

Apply the product rule to $- \frac{11}{2}$ .

${(- 1)}^{2} {(\frac{11}{2})}^{2}$

Step 1.1.2

Apply the product rule to $\frac{11}{2}$ .

${(- 1)}^{2} \frac{11^{2}}{2^{2}}$

Step 1.2

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

$1 \frac{11^{2}}{2^{2}}$

Step 1.3

Multiply $\frac{11^{2}}{2^{2}}$ by $1$ .

$\frac{11^{2}}{2^{2}}$

Step 1.4

Raise $11$ to the power of $2$ .

$\frac{121}{2^{2}}$

Step 1.5

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

$\frac{121}{4}$

Step 2

Add $\frac{121}{4}$ to get the perfect square trinomial.

$x^{2} - 11 x + \frac{121}{4}$