Precalculus Examples

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

Step 1

Simplify the left side ${(x + 7)}^{2} + y^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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

Step 1.1.2

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

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Step 1.1.2.1

Apply the distributive property.

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

Step 1.1.2.2

Apply the distributive property.

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

Step 1.1.2.3

Apply the distributive property.

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

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 $x$ by $x$ .

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

Step 1.1.3.1.2

Move $7$ to the left of $x$ .

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

Step 1.1.3.1.3

Multiply $7$ by $7$ .

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

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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