Finite Math Examples

$2 x y - \sqrt{2} x - \frac{1}{2} = 0$

Step 1

Move all terms not containing $y$ to the right side of the equation.

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Step 1.1

Add $\sqrt{2} x$ to both sides of the equation.

$2 x y - \frac{1}{2} = \sqrt{2} x$

Step 1.2

Add $\frac{1}{2}$ to both sides of the equation.

$2 x y = \sqrt{2} x + \frac{1}{2}$

Step 2

Divide each term in $2 x y = \sqrt{2} x + \frac{1}{2}$ by $2 x$ and simplify.

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Step 2.1

Divide each term in $2 x y = \sqrt{2} x + \frac{1}{2}$ by $2 x$ .

$\frac{2 x y}{2 x} = \frac{\sqrt{2} x}{2 x} + \frac{\frac{1}{2}}{2 x}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 x y}{2 x} = \frac{\sqrt{2} x}{2 x} + \frac{\frac{1}{2}}{2 x}$

Step 2.2.1.2

Rewrite the expression.

$\frac{x y}{x} = \frac{\sqrt{2} x}{2 x} + \frac{\frac{1}{2}}{2 x}$

Step 2.2.2

Cancel the common factor of $x$ .

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Step 2.2.2.1

Cancel the common factor.

$\frac{x y}{x} = \frac{\sqrt{2} x}{2 x} + \frac{\frac{1}{2}}{2 x}$

Step 2.2.2.2

Divide $y$ by $1$ .

$y = \frac{\sqrt{2} x}{2 x} + \frac{\frac{1}{2}}{2 x}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $x$ .

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Step 2.3.1.1.1

Cancel the common factor.

$y = \frac{\sqrt{2} x}{2 x} + \frac{\frac{1}{2}}{2 x}$

Step 2.3.1.1.2

Rewrite the expression.

$y = \frac{\sqrt{2}}{2} + \frac{\frac{1}{2}}{2 x}$

Step 2.3.1.2

Multiply the numerator by the reciprocal of the denominator.

$y = \frac{\sqrt{2}}{2} + \frac{1}{2} \cdot \frac{1}{2 x}$

Step 2.3.1.3

Multiply $\frac{1}{2} \cdot \frac{1}{2 x}$ .

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Step 2.3.1.3.1

Multiply $\frac{1}{2}$ by $\frac{1}{2 x}$ .

$y = \frac{\sqrt{2}}{2} + \frac{1}{2 (2 x)}$

Step 2.3.1.3.2

Multiply $2$ by $2$ .

$y = \frac{\sqrt{2}}{2} + \frac{1}{4 x}$