Precalculus Examples

${(x - 0.3)}^{2} + {(y - 3.2)}^{2} = 10 - 1$

Step 1

Simplify the left side ${(x - 0.3)}^{2} + {(y - 3.2)}^{2}$ .

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Simplify each term.

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Rewrite ${(x - 0.3)}^{2}$ as $(x - 0.3) (x - 0.3)$ .

$(x - 0.3) (x - 0.3) + {(y - 3.2)}^{2} = 10 - 1$

Expand $(x - 0.3) (x - 0.3)$ using the FOIL Method.

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Apply the distributive property.

$x (x - 0.3) - 0.3 (x - 0.3) + {(y - 3.2)}^{2} = 10 - 1$

Apply the distributive property.

$x \cdot x + x \cdot - 0.3 - 0.3 (x - 0.3) + {(y - 3.2)}^{2} = 10 - 1$

Apply the distributive property.

$x \cdot x + x \cdot - 0.3 - 0.3 x - 0.3 \cdot - 0.3 + {(y - 3.2)}^{2} = 10 - 1$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

$x^{2} + x \cdot - 0.3 - 0.3 x - 0.3 \cdot - 0.3 + {(y - 3.2)}^{2} = 10 - 1$

Move $- 0.3$ to the left of $x$ .

$x^{2} - 0.3 \cdot x - 0.3 x - 0.3 \cdot - 0.3 + {(y - 3.2)}^{2} = 10 - 1$

Multiply $- 0.3$ by $- 0.3$ .

$x^{2} - 0.3 x - 0.3 x + 0.09 + {(y - 3.2)}^{2} = 10 - 1$

Subtract $0.3 x$ from $- 0.3 x$ .

$x^{2} - 0.6 x + 0.09 + {(y - 3.2)}^{2} = 10 - 1$

Rewrite ${(y - 3.2)}^{2}$ as $(y - 3.2) (y - 3.2)$ .

$x^{2} - 0.6 x + 0.09 + (y - 3.2) (y - 3.2) = 10 - 1$

Expand $(y - 3.2) (y - 3.2)$ using the FOIL Method.

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Apply the distributive property.

$x^{2} - 0.6 x + 0.09 + y (y - 3.2) - 3.2 (y - 3.2) = 10 - 1$

Apply the distributive property.

$x^{2} - 0.6 x + 0.09 + y \cdot y + y \cdot - 3.2 - 3.2 (y - 3.2) = 10 - 1$

Apply the distributive property.

$x^{2} - 0.6 x + 0.09 + y \cdot y + y \cdot - 3.2 - 3.2 y - 3.2 \cdot - 3.2 = 10 - 1$

Simplify and combine like terms.

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Simplify each term.

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Multiply $y$ by $y$ .

$x^{2} - 0.6 x + 0.09 + y^{2} + y \cdot - 3.2 - 3.2 y - 3.2 \cdot - 3.2 = 10 - 1$

Move $- 3.2$ to the left of $y$ .

$x^{2} - 0.6 x + 0.09 + y^{2} - 3.2 \cdot y - 3.2 y - 3.2 \cdot - 3.2 = 10 - 1$

Multiply $- 3.2$ by $- 3.2$ .

$x^{2} - 0.6 x + 0.09 + y^{2} - 3.2 y - 3.2 y + 10.24 = 10 - 1$

Subtract $3.2 y$ from $- 3.2 y$ .

$x^{2} - 0.6 x + 0.09 + y^{2} - 6.4 y + 10.24 = 10 - 1$

Simplify the expression.

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Add $0.09$ and $10.24$ .

$x^{2} - 0.6 x + y^{2} - 6.4 y + 10.33 = 10 - 1$

Move $- 0.6 x$ .

$x^{2} + y^{2} - 0.6 x - 6.4 y + 10.33 = 10 - 1$

Step 2

Subtract $1$ from $10$ .

$x^{2} + y^{2} - 0.6 x - 6.4 y + 10.33 = 9$

Step 3

Subtract $9$ from both sides of the equation.

$x^{2} + y^{2} - 0.6 x - 6.4 y + 10.33 - 9 = 0$

Step 4

Subtract $9$ from $10.33$ .

$x^{2} + y^{2} - 0.6 x - 6.4 y + 1.33 = 0$

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