Precalculus Examples

${(x - 0.01)}^{2} + {(2.202 - y)}^{2} = 25$

Simplify the left side ${(x - 0.01)}^{2} + {(2.202 - y)}^{2}$ .

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Simplify each term.

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Rewrite ${(x - 0.01)}^{2}$ as $(x - 0.01) (x - 0.01)$ .

$(x - 0.01) (x - 0.01) + {(2.202 - y)}^{2} = 25$

Expand $(x - 0.01) (x - 0.01)$ using the FOIL Method.

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Apply the distributive property.

$x (x - 0.01) - 0.01 (x - 0.01) + {(2.202 - y)}^{2} = 25$

Apply the distributive property.

$x x + x \cdot - 0.01 - 0.01 (x - 0.01) + {(2.202 - y)}^{2} = 25$

Apply the distributive property.

$x x + x \cdot - 0.01 + (- 0.01 x - 0.01 \cdot - 0.01) + {(2.202 - y)}^{2} = 25$

Remove parentheses.

$x x + x \cdot - 0.01 - 0.01 x - 0.01 \cdot - 0.01 + {(2.202 - y)}^{2} = 25$

Simplify and combine like terms.

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Simplify each term.

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Simplify $x^{1 + 1}$ .

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Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{1 + 1} + x \cdot - 0.01 - 0.01 x - 0.01 \cdot - 0.01 + {(2.202 - y)}^{2} = 25$

Add $1$ and $1$ .

$x^{2} + x \cdot - 0.01 - 0.01 x - 0.01 \cdot - 0.01 + {(2.202 - y)}^{2} = 25$

Move $- 0.01$ to the left of the expression $x \cdot - 0.01$ .

$x^{2} - 0.01 \cdot x - 0.01 x - 0.01 \cdot - 0.01 + {(2.202 - y)}^{2} = 25$

Multiply $- 0.01$ by $x$ .

$x^{2} - 0.01 x - 0.01 x - 0.01 \cdot - 0.01 + {(2.202 - y)}^{2} = 25$

Multiply $- 0.01$ by $- 0.01$ .

$x^{2} - 0.01 x - 0.01 x + 0.0001 + {(2.202 - y)}^{2} = 25$

Subtract $0.01 x$ from $- 0.01 x$ .

$x^{2} - 0.02 x + 0.0001 + {(2.202 - y)}^{2} = 25$

Rewrite ${(2.202 - y)}^{2}$ as $(2.202 - y) (2.202 - y)$ .

$x^{2} - 0.02 x + 0.0001 + (2.202 - y) (2.202 - y) = 25$

Expand $(2.202 - y) (2.202 - y)$ using the FOIL Method.

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Apply the distributive property.

$x^{2} - 0.02 x + 0.0001 + (2.202 (2.202 - y) - y (2.202 - y)) = 25$

Apply the distributive property.

$x^{2} - 0.02 x + 0.0001 + (2.202 \cdot 2.202 + 2.202 (- y) - y (2.202 - y)) = 25$

Apply the distributive property.

$x^{2} - 0.02 x + 0.0001 + (2.202 \cdot 2.202 + 2.202 (- y) + (- y \cdot 2.202 - y (- y))) = 25$

Remove parentheses.

$x^{2} - 0.02 x + 0.0001 + (2.202 \cdot 2.202 + 2.202 (- y) - y \cdot 2.202 - y (- y)) = 25$

Simplify and combine like terms.

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Simplify each term.

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Multiply $2.202$ by $2.202$ .

$x^{2} - 0.02 x + 0.0001 + (4.848804 + 2.202 (- y) - y \cdot 2.202 - y (- y)) = 25$

Multiply $- 1$ by $2.202$ .

$x^{2} - 0.02 x + 0.0001 + (4.848804 - 2.202 y - y \cdot 2.202 - y (- y)) = 25$

Multiply $2.202$ by $- 1$ .

$x^{2} - 0.02 x + 0.0001 + (4.848804 - 2.202 y - 2.202 y - y (- y)) = 25$

Move $y$ .

$x^{2} - 0.02 x + 0.0001 + (4.848804 - 2.202 y - 2.202 y - 1 (- (y y))) = 25$

Simplify $y^{1 + 1}$ .

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Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2} - 0.02 x + 0.0001 + (4.848804 - 2.202 y - 2.202 y - 1 (- y^{1 + 1})) = 25$

Add $1$ and $1$ .

$x^{2} - 0.02 x + 0.0001 + (4.848804 - 2.202 y - 2.202 y - 1 (- y^{2})) = 25$

Simplify $- 1 (- y^{2})$ .

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Multiply $- 1$ by $- 1$ .

$x^{2} - 0.02 x + 0.0001 + (4.848804 - 2.202 y - 2.202 y + 1 y^{2}) = 25$

Multiply $y^{2}$ by $1$ .

$x^{2} - 0.02 x + 0.0001 + (4.848804 - 2.202 y - 2.202 y + y^{2}) = 25$

Subtract $2.202 y$ from $- 2.202 y$ .

$x^{2} - 0.02 x + 0.0001 + (4.848804 - 4.404 y + y^{2}) = 25$

Simplify the expression.

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Remove unnecessary parentheses.

$x^{2} - 0.02 x + 0.0001 + 4.848804 - 4.404 y + y^{2} = 25$

Add $0.0001$ and $4.848804$ .

$x^{2} - 0.02 x + 4.848904 - 4.404 y + y^{2} = 25$

Move $25$ to the left side of the equation by subtracting it from both sides.

$x^{2} - 0.02 x + 4.848904 - 4.404 y + y^{2} - 25 = 0$

Subtract $25$ from $4.848904$ .

$x^{2} - 0.02 x - 4.404 y + y^{2} - 20.151096 = 0$

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