Finite Math Examples

$y^{2} = 6 x$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{6 x}$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{6 x}$

Step 2.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{6 x}$

Step 2.3

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{6 x}$

$y = - \sqrt{6 x}$

$y = \sqrt{6 x}$

$y = - \sqrt{6 x}$

Step 3

Set the radicand in $\sqrt{6 x}$ greater than or equal to $0$ to find where the expression is defined.

$6 x \geq 0$

Step 4

Divide each term in $6 x \geq 0$ by $6$ and simplify.

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Step 4.1

Divide each term in $6 x \geq 0$ by $6$ .

$\frac{6 x}{6} \geq \frac{0}{6}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $6$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{6 x}{6} \geq \frac{0}{6}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x \geq \frac{0}{6}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $6$ .

$x \geq 0$

Step 5

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 6