Examples

{(x + 7)}^{2} + y^{2} = 81

${(x + 7)}^{2} + y^{2} = 81$

Step 1

Simplify the left side

{(x + 7)}^{2} + y^{2}

${(x + 7)}^{2} + y^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite

{(x + 7)}^{2}

${(x + 7)}^{2}$ as

(x + 7) (x + 7)

$(x + 7) (x + 7)$ .

(x + 7) (x + 7) + y^{2} = 81

$(x + 7) (x + 7) + y^{2} = 81$

Step 1.1.2

Expand

(x + 7) (x + 7)

$(x + 7) (x + 7)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

x (x + 7) + 7 (x + 7) + y^{2} = 81

$x (x + 7) + 7 (x + 7) + y^{2} = 81$

Step 1.1.2.2

Apply the distributive property.

x \cdot x + x \cdot 7 + 7 (x + 7) + y^{2} = 81

$x \cdot x + x \cdot 7 + 7 (x + 7) + y^{2} = 81$

Step 1.1.2.3

Apply the distributive property.

x \cdot x + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81

$x \cdot x + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81$

x \cdot x + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81

$x \cdot x + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81$

Step 1.1.3

Simplify and combine like terms.

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Step 1.1.3.1

Simplify each term.

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Step 1.1.3.1.1

Multiply

x

$x$ by

x

$x$ .

x^{2} + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81

$x^{2} + x \cdot 7 + 7 x + 7 \cdot 7 + y^{2} = 81$

Step 1.1.3.1.2

Move

7

$7$ to the left of

x

$x$ .

x^{2} + 7 \cdot x + 7 x + 7 \cdot 7 + y^{2} = 81

$x^{2} + 7 \cdot x + 7 x + 7 \cdot 7 + y^{2} = 81$

Step 1.1.3.1.3

Multiply

7

$7$ by

7

$7$ .

x^{2} + 7 x + 7 x + 49 + y^{2} = 81

$x^{2} + 7 x + 7 x + 49 + y^{2} = 81$

x^{2} + 7 x + 7 x + 49 + y^{2} = 81

$x^{2} + 7 x + 7 x + 49 + y^{2} = 81$

Step 1.1.3.2

Add

$7 x$ and

$7 x$ .

$x^{2} + 14 x + 49 + y^{2} = 81$

Step 1.2

Reorder.

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Step 1.2.1

Move

$49$ .

$x^{2} + 14 x + y^{2} + 49 = 81$

Step 1.2.2

Move

$14 x$ .

$x^{2} + y^{2} + 14 x + 49 = 81$

Step 2

Subtract

$81$ from both sides of the equation.

$x^{2} + y^{2} + 14 x + 49 - 81 = 0$

Step 3

Subtract

$81$ from

$49$ .

$x^{2} + y^{2} + 14 x - 32 = 0$

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