Calculus Examples

$y = \sqrt{x^{2 - 2} c y}$

Step 1

Rewrite the equation as $\sqrt{x^{2 - 2} c y} = y$ .

$\sqrt{x^{2 - 2} c y} = y$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{x^{2 - 2} c y}}^{2} = y^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x^{2 - 2} c y}$ as ${(x^{2 - 2} c y)}^{\frac{1}{2}}$ .

${({(x^{2 - 2} c y)}^{\frac{1}{2}})}^{2} = y^{2}$

Step 3.2

Subtract $2$ from $2$ .

${({(x^{0} c y)}^{\frac{1}{2}})}^{2} = y^{2}$

Step 3.3

Simplify the left side.

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Step 3.3.1

Simplify ${({(x^{0} c y)}^{\frac{1}{2}})}^{2}$ .

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Step 3.3.1.1

Multiply the exponents in ${({(x^{0} c y)}^{\frac{1}{2}})}^{2}$ .

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Step 3.3.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(x^{0} c y)}^{\frac{1}{2} \cdot 2} = y^{2}$

Step 3.3.1.1.2

Cancel the common factor of $2$ .

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Step 3.3.1.1.2.1

Cancel the common factor.

${(x^{0} c y)}^{\frac{1}{2} \cdot 2} = y^{2}$

Step 3.3.1.1.2.2

Rewrite the expression.

${(x^{0} c y)}^{1} = y^{2}$

Step 3.3.1.2

Anything raised to $0$ is $1$ .

${(1 c y)}^{1} = y^{2}$

Step 3.3.1.3

Multiply $c$ by $1$ .

${(c y)}^{1} = y^{2}$

Step 3.3.1.4

Simplify.

$c y = y^{2}$

Step 4

Divide each term in $c y = y^{2}$ by $y$ and simplify.

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Step 4.1

Divide each term in $c y = y^{2}$ by $y$ .

$\frac{c y}{y} = \frac{y^{2}}{y}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $y$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{c y}{y} = \frac{y^{2}}{y}$

Step 4.2.1.2

Divide $c$ by $1$ .

$c = \frac{y^{2}}{y}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $y^{2}$ and $y$ .

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Step 4.3.1.1

Factor $y$ out of $y^{2}$ .

$c = \frac{y \cdot y}{y}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Raise $y$ to the power of $1$ .

$c = \frac{y \cdot y}{y^{1}}$

Step 4.3.1.2.2

Factor $y$ out of $y^{1}$ .

$c = \frac{y \cdot y}{y \cdot 1}$

Step 4.3.1.2.3

Cancel the common factor.

$c = \frac{y \cdot y}{y \cdot 1}$

Step 4.3.1.2.4

Rewrite the expression.

$c = \frac{y}{1}$

Step 4.3.1.2.5

Divide $y$ by $1$ .

$c = y$

Step 5

The variable $x$ got canceled.

All real numbers

Step 6

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$