Algebra Examples

${(x - 0.1)}^{2} + {(2.2 - y)}^{2} = 25$

Step 1

Simplify the left side ${(x - 0.1)}^{2} + {(2.2 - y)}^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Rewrite ${(x - 0.1)}^{2}$ as $(x - 0.1) (x - 0.1)$ .

$(x - 0.1) (x - 0.1) + {(2.2 - y)}^{2} = 25$

Step 1.1.2

Expand $(x - 0.1) (x - 0.1)$ using the FOIL Method.

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Step 1.1.2.1

Apply the distributive property.

$x (x - 0.1) - 0.1 (x - 0.1) + {(2.2 - y)}^{2} = 25$

Step 1.1.2.2

Apply the distributive property.

$x \cdot x + x \cdot - 0.1 - 0.1 (x - 0.1) + {(2.2 - y)}^{2} = 25$

Step 1.1.2.3

Apply the distributive property.

$x \cdot x + x \cdot - 0.1 - 0.1 x - 0.1 \cdot - 0.1 + {(2.2 - y)}^{2} = 25$

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 $x$ .

$x^{2} + x \cdot - 0.1 - 0.1 x - 0.1 \cdot - 0.1 + {(2.2 - y)}^{2} = 25$

Step 1.1.3.1.2

Move $- 0.1$ to the left of $x$ .

$x^{2} - 0.1 \cdot x - 0.1 x - 0.1 \cdot - 0.1 + {(2.2 - y)}^{2} = 25$

Step 1.1.3.1.3

Multiply $- 0.1$ by $- 0.1$ .

$x^{2} - 0.1 x - 0.1 x + 0.01 + {(2.2 - y)}^{2} = 25$

Step 1.1.3.2

Subtract $0.1 x$ from $- 0.1 x$ .

$x^{2} - 0.2 x + 0.01 + {(2.2 - y)}^{2} = 25$

Step 1.1.4

Rewrite ${(2.2 - y)}^{2}$ as $(2.2 - y) (2.2 - y)$ .

$x^{2} - 0.2 x + 0.01 + (2.2 - y) (2.2 - y) = 25$

Step 1.1.5

Expand $(2.2 - y) (2.2 - y)$ using the FOIL Method.

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Step 1.1.5.1

Apply the distributive property.

$x^{2} - 0.2 x + 0.01 + 2.2 (2.2 - y) - y (2.2 - y) = 25$

Step 1.1.5.2

Apply the distributive property.

$x^{2} - 0.2 x + 0.01 + 2.2 \cdot 2.2 + 2.2 (- y) - y (2.2 - y) = 25$

Step 1.1.5.3

Apply the distributive property.

$x^{2} - 0.2 x + 0.01 + 2.2 \cdot 2.2 + 2.2 (- y) - y \cdot 2.2 - y (- y) = 25$

Step 1.1.6

Simplify and combine like terms.

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Step 1.1.6.1

Simplify each term.

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Step 1.1.6.1.1

Multiply $2.2$ by $2.2$ .

$x^{2} - 0.2 x + 0.01 + 4.84 + 2.2 (- y) - y \cdot 2.2 - y (- y) = 25$

Step 1.1.6.1.2

Multiply $- 1$ by $2.2$ .

$x^{2} - 0.2 x + 0.01 + 4.84 - 2.2 y - y \cdot 2.2 - y (- y) = 25$

Step 1.1.6.1.3

Multiply $2.2$ by $- 1$ .

$x^{2} - 0.2 x + 0.01 + 4.84 - 2.2 y - 2.2 y - y (- y) = 25$

Step 1.1.6.1.4

Rewrite using the commutative property of multiplication.

$x^{2} - 0.2 x + 0.01 + 4.84 - 2.2 y - 2.2 y - 1 \cdot (- 1 y \cdot y) = 25$

Step 1.1.6.1.5

Multiply $y$ by $y$ by adding the exponents.

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Step 1.1.6.1.5.1

Move $y$ .

$x^{2} - 0.2 x + 0.01 + 4.84 - 2.2 y - 2.2 y - 1 \cdot (- 1 (y \cdot y)) = 25$

Step 1.1.6.1.5.2

Multiply $y$ by $y$ .

$x^{2} - 0.2 x + 0.01 + 4.84 - 2.2 y - 2.2 y - 1 \cdot (- 1 y^{2}) = 25$

Step 1.1.6.1.6

Multiply $- 1$ by $- 1$ .

$x^{2} - 0.2 x + 0.01 + 4.84 - 2.2 y - 2.2 y + 1 y^{2} = 25$

Step 1.1.6.1.7

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

$x^{2} - 0.2 x + 0.01 + 4.84 - 2.2 y - 2.2 y + y^{2} = 25$

Step 1.1.6.2

Subtract $2.2 y$ from $- 2.2 y$ .

$x^{2} - 0.2 x + 0.01 + 4.84 - 4.4 y + y^{2} = 25$

Step 1.2

Simplify the expression.

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Step 1.2.1

Add $0.01$ and $4.84$ .

$x^{2} - 0.2 x + 4.85 - 4.4 y + y^{2} = 25$

Step 1.2.2

Move $4.85$ .

$x^{2} - 0.2 x - 4.4 y + y^{2} + 4.85 = 25$

Step 1.2.3

Move $- 4.4 y$ .

$x^{2} - 0.2 x + y^{2} - 4.4 y + 4.85 = 25$

Step 1.2.4

Move $- 0.2 x$ .

$x^{2} + y^{2} - 0.2 x - 4.4 y + 4.85 = 25$

Step 2

Subtract $25$ from both sides of the equation.

$x^{2} + y^{2} - 0.2 x - 4.4 y + 4.85 - 25 = 0$

Step 3

Subtract $25$ from $4.85$ .

$x^{2} + y^{2} - 0.2 x - 4.4 y - 20.15 = 0$

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