Finite Math Examples

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

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

Step 1

Solve the equation for

y

$y$ .

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Step 1.1

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 1.1.1

Add

\sqrt{2} x

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

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

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

Step 1.1.2

Add

\frac{1}{2}

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

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

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

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

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

Step 1.2

Divide each term in

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

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

2 x

$2 x$ and simplify.

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Step 1.2.1

Divide each term in

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

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

2 x

$2 x$ .

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

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of

2

$2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

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

Step 1.2.2.1.2

Rewrite the expression.

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

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

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

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

Step 1.2.2.2

Cancel the common factor of

x

$x$ .

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Step 1.2.2.2.1

Cancel the common factor.

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

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

Step 1.2.2.2.2

Divide

y

$y$ by

1

$1$ .

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

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

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

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

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

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of

x

$x$ .

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Step 1.2.3.1.1.1

Cancel the common factor.

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

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

Step 1.2.3.1.1.2

Rewrite the expression.

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

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

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

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

Step 1.2.3.1.2

Multiply the numerator by the reciprocal of the denominator.

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

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

Step 1.2.3.1.3

Multiply

\frac{1}{2} \cdot \frac{1}{2 x}

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

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Step 1.2.3.1.3.1

Multiply

\frac{1}{2}

$\frac{1}{2}$ by

\frac{1}{2 x}

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

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

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

Step 1.2.3.1.3.2

Multiply

2

$2$ by

2

$2$ .

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