Finite Math Examples

$7 x \sqrt{3} - 5 = 0$

Step 1

Add $5$ to both sides of the equation.

$7 x \sqrt{3} = 5$

Step 2

Divide each term in $7 x \sqrt{3} = 5$ by $7 \sqrt{3}$ and simplify.

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Step 2.1

Divide each term in $7 x \sqrt{3} = 5$ by $7 \sqrt{3}$ .

$\frac{7 x \sqrt{3}}{7 \sqrt{3}} = \frac{5}{7 \sqrt{3}}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $7$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{7 x \sqrt{3}}{7 \sqrt{3}} = \frac{5}{7 \sqrt{3}}$

Step 2.2.1.2

Rewrite the expression.

$\frac{x \sqrt{3}}{\sqrt{3}} = \frac{5}{7 \sqrt{3}}$

Step 2.2.2

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

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Step 2.2.2.1

Cancel the common factor.

$\frac{x \sqrt{3}}{\sqrt{3}} = \frac{5}{7 \sqrt{3}}$

Step 2.2.2.2

Divide $x$ by $1$ .

$x = \frac{5}{7 \sqrt{3}}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply $\frac{5}{7 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$x = \frac{5}{7 \sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}$

Step 2.3.2

Combine and simplify the denominator.

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Step 2.3.2.1

Multiply $\frac{5}{7 \sqrt{3}}$ by $\frac{\sqrt{3}}{\sqrt{3}}$ .

$x = \frac{5 \sqrt{3}}{7 \sqrt{3} \sqrt{3}}$

Step 2.3.2.2

Move $\sqrt{3}$ .

$x = \frac{5 \sqrt{3}}{7 (\sqrt{3} \sqrt{3})}$

Step 2.3.2.3

Raise $\sqrt{3}$ to the power of $1$ .

$x = \frac{5 \sqrt{3}}{7 ({\sqrt{3}}^{1} \sqrt{3})}$

Step 2.3.2.4

Raise $\sqrt{3}$ to the power of $1$ .

$x = \frac{5 \sqrt{3}}{7 ({\sqrt{3}}^{1} {\sqrt{3}}^{1})}$

Step 2.3.2.5

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x = \frac{5 \sqrt{3}}{7 {\sqrt{3}}^{1 + 1}}$

Step 2.3.2.6

Add $1$ and $1$ .

$x = \frac{5 \sqrt{3}}{7 {\sqrt{3}}^{2}}$

Step 2.3.2.7

Rewrite ${\sqrt{3}}^{2}$ as $3$ .

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Step 2.3.2.7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

$x = \frac{5 \sqrt{3}}{7 {(3^{\frac{1}{2}})}^{2}}$

Step 2.3.2.7.2

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

$x = \frac{5 \sqrt{3}}{7 \cdot 3^{\frac{1}{2} \cdot 2}}$

Step 2.3.2.7.3

Combine $\frac{1}{2}$ and $2$ .

$x = \frac{5 \sqrt{3}}{7 \cdot 3^{\frac{2}{2}}}$

Step 2.3.2.7.4

Cancel the common factor of $2$ .

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Step 2.3.2.7.4.1

Cancel the common factor.

$x = \frac{5 \sqrt{3}}{7 \cdot 3^{\frac{2}{2}}}$

Step 2.3.2.7.4.2

Rewrite the expression.

$x = \frac{5 \sqrt{3}}{7 \cdot 3^{1}}$

Step 2.3.2.7.5

Evaluate the exponent.

$x = \frac{5 \sqrt{3}}{7 \cdot 3}$

Step 2.3.3

Multiply $7$ by $3$ .

$x = \frac{5 \sqrt{3}}{21}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{5 \sqrt{3}}{21}$

Decimal Form:

$x = 0.41239304 \dots$