Pre-Algebra Examples

$x = \frac{{(3 x)}^{2}}{4 \sqrt{3}}$

Step 1

Multiply both sides by $4 \sqrt{3}$ .

$x (4 \sqrt{3}) = \frac{{(3 x)}^{2}}{4 \sqrt{3}} (4 \sqrt{3})$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Move $4$ to the left of $x$ .

$4 x \sqrt{3} = \frac{{(3 x)}^{2}}{4 \sqrt{3}} (4 \sqrt{3})$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{{(3 x)}^{2}}{4 \sqrt{3}} (4 \sqrt{3})$ .

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Step 2.2.1.1

Cancel the common factor of $4 \sqrt{3}$ .

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Step 2.2.1.1.1

Cancel the common factor.

$4 x \sqrt{3} = \frac{{(3 x)}^{2}}{4 \sqrt{3}} (4 \sqrt{3})$

Step 2.2.1.1.2

Rewrite the expression.

$4 x \sqrt{3} = {(3 x)}^{2}$

Step 2.2.1.2

Simplify the expression.

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Step 2.2.1.2.1

Apply the product rule to $3 x$ .

$4 x \sqrt{3} = 3^{2} x^{2}$

Step 2.2.1.2.2

Raise $3$ to the power of $2$ .

$4 x \sqrt{3} = 9 x^{2}$

Step 3

Solve for $x$ .

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Step 3.1

Subtract $9 x^{2}$ from both sides of the equation.

$4 x \sqrt{3} - 9 x^{2} = 0$

Step 3.2

Factor $x$ out of $4 x \sqrt{3} - 9 x^{2}$ .

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Step 3.2.1

Factor $x$ out of $4 x \sqrt{3}$ .

$x (4 \sqrt{3}) - 9 x^{2} = 0$

Step 3.2.2

Factor $x$ out of $- 9 x^{2}$ .

$x (4 \sqrt{3}) + x (- 9 x) = 0$

Step 3.2.3

Factor $x$ out of $x (4 \sqrt{3}) + x (- 9 x)$ .

$x (4 \sqrt{3} - 9 x) = 0$

Step 3.3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$4 \sqrt{3} - 9 x = 0$

Step 3.4

Set $x$ equal to $0$ .

$x = 0$

Step 3.5

Set $4 \sqrt{3} - 9 x$ equal to $0$ and solve for $x$ .

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Step 3.5.1

Set $4 \sqrt{3} - 9 x$ equal to $0$ .

$4 \sqrt{3} - 9 x = 0$

Step 3.5.2

Solve $4 \sqrt{3} - 9 x = 0$ for $x$ .

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Step 3.5.2.1

Subtract $4 \sqrt{3}$ from both sides of the equation.

$- 9 x = - 4 \sqrt{3}$

Step 3.5.2.2

Divide each term in $- 9 x = - 4 \sqrt{3}$ by $- 9$ and simplify.

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Step 3.5.2.2.1

Divide each term in $- 9 x = - 4 \sqrt{3}$ by $- 9$ .

$\frac{- 9 x}{- 9} = \frac{- 4 \sqrt{3}}{- 9}$

Step 3.5.2.2.2

Simplify the left side.

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Step 3.5.2.2.2.1

Cancel the common factor of $- 9$ .

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Step 3.5.2.2.2.1.1

Cancel the common factor.

$\frac{- 9 x}{- 9} = \frac{- 4 \sqrt{3}}{- 9}$

Step 3.5.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 4 \sqrt{3}}{- 9}$

Step 3.5.2.2.3

Simplify the right side.

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Step 3.5.2.2.3.1

Dividing two negative values results in a positive value.

$x = \frac{4 \sqrt{3}}{9}$

Step 3.6

The final solution is all the values that make $x (4 \sqrt{3} - 9 x) = 0$ true.

$x = 0, \frac{4 \sqrt{3}}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = 0, \frac{4 \sqrt{3}}{9}$

Decimal Form:

$x = 0, 0.76980035 \dots$