Find the Expanded Form (x-1/7)^2+y^2=1/49

${(x - \frac{1}{7})}^{2} + y^{2} = \frac{1}{49}$

Step 1

Simplify the left side ${(x - \frac{1}{7})}^{2} + y^{2}$ .

Simplify each term.

Rewrite ${(x - \frac{1}{7})}^{2}$ as $(x - \frac{1}{7}) (x - \frac{1}{7})$ .

$(x - \frac{1}{7}) (x - \frac{1}{7}) + y^{2} = \frac{1}{49}$

Expand $(x - \frac{1}{7}) (x - \frac{1}{7})$ using the FOIL Method.

Apply the distributive property.

$x (x - \frac{1}{7}) - \frac{1}{7} \cdot (x - \frac{1}{7}) + y^{2} = \frac{1}{49}$

Apply the distributive property.

$x \cdot x + x (- \frac{1}{7}) - \frac{1}{7} \cdot (x - \frac{1}{7}) + y^{2} = \frac{1}{49}$

Apply the distributive property.

$x \cdot x + x (- \frac{1}{7}) - \frac{1}{7} x - \frac{1}{7} \cdot (- \frac{1}{7}) + y^{2} = \frac{1}{49}$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x (- \frac{1}{7}) - \frac{1}{7} x - \frac{1}{7} \cdot (- \frac{1}{7}) + y^{2} = \frac{1}{49}$

Combine $x$ and $\frac{1}{7}$ .

$x^{2} - \frac{x}{7} - \frac{1}{7} x - \frac{1}{7} \cdot (- \frac{1}{7}) + y^{2} = \frac{1}{49}$

Combine $x$ and $\frac{1}{7}$ .

$x^{2} - \frac{x}{7} - \frac{x}{7} - \frac{1}{7} \cdot (- \frac{1}{7}) + y^{2} = \frac{1}{49}$

Multiply $- \frac{1}{7} (- \frac{1}{7})$ .

Multiply $- 1$ by $- 1$ .

$x^{2} - \frac{x}{7} - \frac{x}{7} + 1 (\frac{1}{7}) \cdot \frac{1}{7} + y^{2} = \frac{1}{49}$

Multiply $\frac{1}{7}$ by $1$ .

$x^{2} - \frac{x}{7} - \frac{x}{7} + \frac{1}{7} \cdot \frac{1}{7} + y^{2} = \frac{1}{49}$

Multiply $\frac{1}{7}$ by $\frac{1}{7}$ .

$x^{2} - \frac{x}{7} - \frac{x}{7} + \frac{1}{7 \cdot 7} + y^{2} = \frac{1}{49}$

Multiply $7$ by $7$ .

$x^{2} - \frac{x}{7} - \frac{x}{7} + \frac{1}{49} + y^{2} = \frac{1}{49}$

Subtract $\frac{x}{7}$ from $- \frac{x}{7}$ .

$x^{2} - 2 \frac{x}{7} + \frac{1}{49} + y^{2} = \frac{1}{49}$

Simplify each term.

Combine $- 2$ and $\frac{x}{7}$ .

$x^{2} + \frac{- 2 x}{7} + \frac{1}{49} + y^{2} = \frac{1}{49}$

Move the negative in front of the fraction.

$x^{2} - \frac{2 x}{7} + \frac{1}{49} + y^{2} = \frac{1}{49}$

Reorder.

Move $\frac{1}{49}$ .

$x^{2} - \frac{2 x}{7} + y^{2} + \frac{1}{49} = \frac{1}{49}$

Move $- \frac{2 x}{7}$ .

$x^{2} + y^{2} - \frac{2 x}{7} + \frac{1}{49} = \frac{1}{49}$

Step 2

Subtract $\frac{1}{49}$ from both sides of the equation.

$x^{2} + y^{2} - \frac{2 x}{7} + \frac{1}{49} - \frac{1}{49} = 0$

Step 3

Combine the opposite terms in $x^{2} + y^{2} - \frac{2 x}{7} + \frac{1}{49} - \frac{1}{49}$ .

Combine the numerators over the common denominator.

$x^{2} + y^{2} - \frac{2 x}{7} + \frac{1 - 1}{49} = 0$

Subtract $1$ from $1$ .

$x^{2} + y^{2} - \frac{2 x}{7} + \frac{0}{49} = 0$

Divide $0$ by $49$ .

$x^{2} + y^{2} - \frac{2 x}{7} + 0 = 0$

Add $x^{2} + y^{2} - \frac{2 x}{7}$ and $0$ .

$x^{2} + y^{2} - \frac{2 x}{7} = 0$

Find the Expanded Form (x-1/7)^2+y^2=1/49

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