Algebra Examples

${(x - \frac{1}{6})}^{2} + y^{2} = \frac{1}{36}$

Step 1

Simplify the left side ${(x - \frac{1}{6})}^{2} + y^{2}$ .

Tap for more steps...

Step 1.1

Simplify each term.

Tap for more steps...

Step 1.1.1

Rewrite ${(x - \frac{1}{6})}^{2}$ as $(x - \frac{1}{6}) (x - \frac{1}{6})$ .

$(x - \frac{1}{6}) (x - \frac{1}{6}) + y^{2} = \frac{1}{36}$

Step 1.1.2

Expand $(x - \frac{1}{6}) (x - \frac{1}{6})$ using the FOIL Method.

Tap for more steps...

Step 1.1.2.1

Apply the distributive property.

$x (x - \frac{1}{6}) - \frac{1}{6} \cdot (x - \frac{1}{6}) + y^{2} = \frac{1}{36}$

Step 1.1.2.2

Apply the distributive property.

$x \cdot x + x (- \frac{1}{6}) - \frac{1}{6} \cdot (x - \frac{1}{6}) + y^{2} = \frac{1}{36}$

Step 1.1.2.3

Apply the distributive property.

$x \cdot x + x (- \frac{1}{6}) - \frac{1}{6} x - \frac{1}{6} \cdot (- \frac{1}{6}) + y^{2} = \frac{1}{36}$

Step 1.1.3

Simplify and combine like terms.

Tap for more steps...

Step 1.1.3.1

Simplify each term.

Tap for more steps...

Step 1.1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x (- \frac{1}{6}) - \frac{1}{6} x - \frac{1}{6} \cdot (- \frac{1}{6}) + y^{2} = \frac{1}{36}$

Step 1.1.3.1.2

Combine $x$ and $\frac{1}{6}$ .

$x^{2} - \frac{x}{6} - \frac{1}{6} x - \frac{1}{6} \cdot (- \frac{1}{6}) + y^{2} = \frac{1}{36}$

Step 1.1.3.1.3

Combine $x$ and $\frac{1}{6}$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} - \frac{1}{6} \cdot (- \frac{1}{6}) + y^{2} = \frac{1}{36}$

Step 1.1.3.1.4

Multiply $- \frac{1}{6} (- \frac{1}{6})$ .

Tap for more steps...

Step 1.1.3.1.4.1

Multiply $- 1$ by $- 1$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} + 1 (\frac{1}{6}) \cdot \frac{1}{6} + y^{2} = \frac{1}{36}$

Step 1.1.3.1.4.2

Multiply $\frac{1}{6}$ by $1$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} + \frac{1}{6} \cdot \frac{1}{6} + y^{2} = \frac{1}{36}$

Step 1.1.3.1.4.3

Multiply $\frac{1}{6}$ by $\frac{1}{6}$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} + \frac{1}{6 \cdot 6} + y^{2} = \frac{1}{36}$

Step 1.1.3.1.4.4

Multiply $6$ by $6$ .

$x^{2} - \frac{x}{6} - \frac{x}{6} + \frac{1}{36} + y^{2} = \frac{1}{36}$

Step 1.1.3.2

Subtract $\frac{x}{6}$ from $- \frac{x}{6}$ .

$x^{2} - 2 \frac{x}{6} + \frac{1}{36} + y^{2} = \frac{1}{36}$

Step 1.1.4

Simplify each term.

Tap for more steps...

Step 1.1.4.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.4.1.1

Factor $2$ out of $- 2$ .

$x^{2} + 2 (- 1) (\frac{x}{6}) + \frac{1}{36} + y^{2} = \frac{1}{36}$

Step 1.1.4.1.2

Factor $2$ out of $6$ .

$x^{2} + 2 \cdot (- 1 \frac{x}{2 \cdot 3}) + \frac{1}{36} + y^{2} = \frac{1}{36}$

Step 1.1.4.1.3

Cancel the common factor.

$x^{2} + 2 \cdot (- 1 \frac{x}{2 \cdot 3}) + \frac{1}{36} + y^{2} = \frac{1}{36}$

Step 1.1.4.1.4

Rewrite the expression.

$x^{2} - 1 \frac{x}{3} + \frac{1}{36} + y^{2} = \frac{1}{36}$

Step 1.1.4.2

Rewrite $- 1 \frac{x}{3}$ as $- \frac{x}{3}$ .

$x^{2} - \frac{x}{3} + \frac{1}{36} + y^{2} = \frac{1}{36}$

Step 1.2

Reorder.

Tap for more steps...

Step 1.2.1

Move $\frac{1}{36}$ .

$x^{2} - \frac{x}{3} + y^{2} + \frac{1}{36} = \frac{1}{36}$

Step 1.2.2

Move $- \frac{x}{3}$ .

$x^{2} + y^{2} - \frac{x}{3} + \frac{1}{36} = \frac{1}{36}$

Step 2

Subtract $\frac{1}{36}$ from both sides of the equation.

$x^{2} + y^{2} - \frac{x}{3} + \frac{1}{36} - \frac{1}{36} = 0$

Step 3

Combine the opposite terms in $x^{2} + y^{2} - \frac{x}{3} + \frac{1}{36} - \frac{1}{36}$ .

Tap for more steps...

Step 3.1

Combine the numerators over the common denominator.

$x^{2} + y^{2} - \frac{x}{3} + \frac{1 - 1}{36} = 0$

Step 3.2

Subtract $1$ from $1$ .

$x^{2} + y^{2} - \frac{x}{3} + \frac{0}{36} = 0$

Step 3.3

Divide $0$ by $36$ .

$x^{2} + y^{2} - \frac{x}{3} + 0 = 0$

Step 3.4

Add $x^{2} + y^{2} - \frac{x}{3}$ and $0$ .

$x^{2} + y^{2} - \frac{x}{3} = 0$