Precalculus Examples

${(x - 11)}^{2} + \sqrt{{(x - 11)}^{2}} - 2$

Step 1

Simplify each term.

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Step 1.1

Rewrite ${(x - 11)}^{2}$ as $(x - 11) (x - 11)$ .

$(x - 11) (x - 11) + \sqrt{{(x - 11)}^{2}} - 2$

Step 1.2

Expand $(x - 11) (x - 11)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x (x - 11) - 11 (x - 11) + \sqrt{{(x - 11)}^{2}} - 2$

Step 1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 11 - 11 (x - 11) + \sqrt{{(x - 11)}^{2}} - 2$

Step 1.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 11 - 11 x - 11 \cdot - 11 + \sqrt{{(x - 11)}^{2}} - 2$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 11 - 11 x - 11 \cdot - 11 + \sqrt{{(x - 11)}^{2}} - 2$

Step 1.3.1.2

Move $- 11$ to the left of $x$ .

$x^{2} - 11 \cdot x - 11 x - 11 \cdot - 11 + \sqrt{{(x - 11)}^{2}} - 2$

Step 1.3.1.3

Multiply $- 11$ by $- 11$ .

$x^{2} - 11 x - 11 x + 121 + \sqrt{{(x - 11)}^{2}} - 2$

Step 1.3.2

Subtract $11 x$ from $- 11 x$ .

$x^{2} - 22 x + 121 + \sqrt{{(x - 11)}^{2}} - 2$

Step 1.4

Pull terms out from under the radical, assuming positive real numbers.

$x^{2} - 22 x + 121 + x - 11 - 2$

Step 2

Simplify by adding terms.

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Step 2.1

Add $- 22 x$ and $x$ .

$x^{2} - 21 x + 121 - 11 - 2$

Step 2.2

Simplify by subtracting numbers.

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Step 2.2.1

Subtract $11$ from $121$ .

$x^{2} - 21 x + 110 - 2$

Step 2.2.2

Subtract $2$ from $110$ .

$x^{2} - 21 x + 108$